Edit Profile Shparlinski, Igor E. Compute Distance To: Compute Author ID: shparlinski.igor-e Published as: Shparlinksi, Igor E.; Shparlinski, I.; Shparlinski, I. E.; Shparlinski, Igor; Shparlinski, Igor E.; Shparlinski, Igor. E.; Shparlinskii, I. E.; Shparlinskij, I. E.; Shparlinskij, Igor E.; Shparlinskiĭ, I. E.; Spharlinski, Igor E. Homepage: http://web.maths.unsw.edu.au/~igorshparlinski/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp · GND Documents Indexed: 688 Publications since 1978, including 14 Books all top 5 Co-Authors 196 single-authored 77 Luca, Florian 62 Banks, William D. 28 Friedlander, John Benjamin 24 Ostafe, Alina 23 von zur Gathen, Joachim 23 Winterhof, Arne 20 Garaev, Moubariz Z. 20 Konyagin, Sergeĭ Vladimirovich 13 Pomerance, Carl Bernard 13 Sha, Min 12 Niederreiter, Harald 10 Gomez-Perez, Domingo 9 Bourgain, Jean 9 Gutierrez, Jaime 9 Pappalardi, Francesco 9 Stepanov, Sergei Alexandrovich 8 Ahmadi, Omran 8 Lieman, Daniel B. 8 Nguyen, Phong Q. 8 Voloch, José Felipe 7 Blackburn, Simon R. 7 Cilleruelo, Javier 7 El-Mahassni, Edwin D. 7 Karpinski, Marek 7 Mans, Bernard 6 Chang, Mei-Chu 6 Farashahi, Reza Rezaeian 6 Ford, Kevin B. 6 Kerr, Bryce 6 Mérai, László 6 van der Poorten, Alfred J. 6 Zhang, Tianping 5 Balasuriya, Sanka 5 Bernasconi, Anna 5 Heyman, Randell 5 Liu, Kui 5 Steinfeld, Ron 4 Blake, Ian F. 4 Conflitti, Alessandro 4 Damm, Carsten 4 Everest, Graham Robert 4 González Vasco, María Isabel 4 Griffin, Frances 4 Khan, Mizan R. 4 Kohel, David R. 4 Kosachevskaya, L. L. 4 Lange, Tanja 4 Mullen, Gary L. 4 Munsch, Marc 4 Näslund, Mats 4 Panario, Daniel 4 Shkredov, Il’ya Dmitrievich 4 Sutantyo, Daniel 4 Yau, Kam-hung 4 Zannier, Umberto M. 3 Bordellès, Olivier 3 Broughan, Kevin A. 3 Chen, Changhao 3 Cojocaru, Alina Carmen 3 Dietmann, Rainer 3 Elsholtz, Christian 3 Fouvry, Etienne 3 Macourt, Simon 3 Moree, Pieter 3 Romanovtsev, V. V. 3 Sutherland, Andrew V. 3 Wang, Huaxiong 3 Zumalacárregui, Ana 2 Allender, Eric W. 2 Balog, Antal 2 Canetti, Ran 2 Chan, Tsz Ho 2 Cohen, Stephen D. 2 Contini, Scott 2 Coppersmith, Don 2 D’Andrea, Carlos 2 Dewar, Michael C. 2 Dubickas, Artūras 2 Galiev, V. I. 2 Harcharras, Asma 2 Harman, Glyn 2 Heath-Brown, Roger 2 Howgrave-Graham, Nick A. 2 Kurlberg, Pär 2 Larsen, Michael Jeffrey 2 Lenstra, Arjen K. 2 Levieil, Eric 2 Levin, Mordekhaĭ Borisovich 2 Ling, San 2 Menezes, Alfred J. 2 Murty, Maruti Ram 2 Petridis, Giorgis 2 Polupanov, A. F. 2 Roche-Newton, Oliver 2 Russell, Alexander C. 2 Saidak, Filip 2 Saks, Michael E. 2 Saxena, Nitin 2 Sombra, Martín 2 Stichtenoth, Henning ...and 127 more Co-Authors all top 5 Serials 29 Journal of Number Theory 25 Bulletin of the Australian Mathematical Society 24 Proceedings of the American Mathematical Society 20 Mathematics of Computation 20 Acta Arithmetica 20 Finite Fields and their Applications 13 Designs, Codes and Cryptography 13 The Quarterly Journal of Mathematics 11 Indagationes Mathematicae. New Series 11 Applicable Algebra in Engineering, Communication and Computing 11 International Journal of Number Theory 10 Information Processing Letters 10 Mathematika 9 Periodica Mathematica Hungarica 9 Archiv der Mathematik 9 Canadian Mathematical Bulletin 9 Glasgow Mathematical Journal 9 Michigan Mathematical Journal 9 Monatshefte für Mathematik 9 SIAM Journal on Discrete Mathematics 8 Mathematical Notes 8 Transactions of the American Mathematical Society 8 Experimental Mathematics 7 IEEE Transactions on Information Theory 7 Bulletin of the London Mathematical Society 7 U.S.S.R. Computational Mathematics and Mathematical Physics 7 Bulletin of the Polish Academy of Sciences, Mathematics 7 Journal of Mathematical Cryptology 6 Canadian Journal of Mathematics 6 IMRN. International Mathematics Research Notices 6 Uniform Distribution Theory 5 Rocky Mountain Journal of Mathematics 5 Russian Mathematical Surveys 5 Mathematische Zeitschrift 5 Computational Complexity 5 Journal de Théorie des Nombres de Bordeaux 5 Mathematical Research Letters 4 Matematicheskie Zametki 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Colloquium Mathematicum 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 SIAM Journal on Computing 4 Theoretical Computer Science 4 Journal of Symbolic Computation 4 Journal of Complexity 4 Linear Algebra and its Applications 4 Integers 3 Journal d’Analyse Mathématique 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Problems of Information Transmission 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Advances in Mathematics 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of the London Mathematical Society. Second Series 3 Algorithmica 3 Revista Matemática Iberoamericana 3 Journal of Cryptology 3 Mathematics of the USSR, Sbornik 3 Boletín de la Sociedad Matemática Mexicana. Third Series 3 Annals of Combinatorics 3 Revista Matemática Complutense 3 Journal of the Australian Mathematical Society 3 Contemporary Mathematics 3 Progress in Computer Science and Applied Logic 3 Advances in Mathematics of Communications 2 Discrete Mathematics 2 Israel Journal of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Acta Scientiarum Mathematicarum 2 Czechoslovak Mathematical Journal 2 Functiones et Approximatio. Commentarii Mathematici 2 Illinois Journal of Mathematics 2 Kodai Mathematical Journal 2 Manuscripta Mathematica 2 Pacific Journal of Mathematics 2 Publicationes Mathematicae 2 Journal of Algorithms 2 European Journal of Combinatorics 2 Applied Mathematics Letters 2 Forum Mathematicum 2 Discrete Mathematics and Applications 2 Problemy Peredachi Informatsii 2 Matematicheskiĭ Sbornik 2 Discrete and Continuous Dynamical Systems 2 The Ramanujan Journal 2 Journal of Integer Sequences 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Pure and Applied Mathematics Quarterly 2 Proceedings of the Steklov Institute of Mathematics 2 Research in the Mathematical Sciences 1 Discrete Applied Mathematics 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 1 Journal of Mathematical Physics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annales des Sciences Mathématiques du Québec 1 The Australian Mathematical Society Gazette 1 Bulletin de la Société Mathématique de France 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Journal of Approximation Theory ...and 45 more Serials all top 5 Fields 632 Number theory (11-XX) 136 Information and communication theory, circuits (94-XX) 77 Computer science (68-XX) 51 Algebraic geometry (14-XX) 41 Numerical analysis (65-XX) 28 Combinatorics (05-XX) 24 Dynamical systems and ergodic theory (37-XX) 12 Field theory and polynomials (12-XX) 9 General and overarching topics; collections (00-XX) 7 Commutative algebra (13-XX) 7 Quantum theory (81-XX) 5 Convex and discrete geometry (52-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Operator theory (47-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Abstract harmonic analysis (43-XX) 2 Probability theory and stochastic processes (60-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 518 Publications have been cited 2,821 times in 1,360 Documents Cited by ▼ Year ▼ Recurrence sequences. Zbl 1033.11006Everest, Graham; van der Poorten, Alf; Shparlinski, Igor; Ward, Thomas 86 2003 Character sums with exponential functions and their applications. Zbl 0933.11001Konyagin, S. V.; Shparlinski, I. E. 77 1999 Parameters of integral circulant graphs and periodic quantum dynamics. Zbl 1119.81042Saxena, Nitin; Severini, Simone; Shparlinski, Igor E. 38 2007 Computational and algorithmic problems in finite fields. Zbl 0780.11064Shparlinski, Igor E. 35 1992 Cryptographic applications of analytic number theory. Complexity lower bounds and pseudorandomness. Zbl 1036.94001Shparlinski, I. 29 2003 Graphs with integral spectrum. Zbl 1178.05060Ahmadi, Omran; Alon, Noga; Blake, Ian F.; Shparlinski, Igor E. 28 2009 Finite fields: theory and computation. The meeting point of number theory, computer science, coding theory and cryptography. Zbl 0967.11052Shparlinski, I. E. 26 1999 On the hidden shifted power problem. Zbl 1311.11111Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 25 2012 On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping. Zbl 1038.94007Coppersmith, Don; Shparlinski, Igor 24 2000 Pseudorandomness and dynamics of Fermat quotients. Zbl 1263.11003Ostafe, Alina; Shparlinski, Igor E. 23 2011 On the distribution of inversive congruential pseudorandom numbers in parts of the period. Zbl 0983.11048Niederreiter, Harald; Shparlinski, Igor E. 23 2001 On the concentration of points of polynomial maps and applications. Zbl 1285.11027Cilleruelo, Javier; Garaev, Moubariz Z.; Ostafe, Alina; Shparlinski, Igor E. 22 2012 Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. Zbl 1250.11064Banks, William D.; Shparlinski, Igor E. 22 2009 On the statistical properties of Diffie-Hellman distributions. Zbl 0997.11066Canetti, Ran; Friedlander, John; Konyagin, Sergei; Larsen, Michael; Lieman, Daniel; Shparlinski, Igor 22 2000 On the cycle structure of repeated exponentiation modulo a prime. Zbl 1060.11059Chou, Wun-Seng; Shparlinski, Igor E. 21 2004 Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm. Zbl 1232.11003Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 20 2008 Recent advances in the theory of nonlinear pseudorandom number generators. Zbl 1076.65008Niederreiter, Harald; Shparlinski, Igor E. 20 2002 Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 20 2002 Character sums with exponential functions. Zbl 1017.11045Friedlander, John B.; Hansen, Jan; Shparlinski, Igor E. 20 2000 Curves with many points and multiplication in finite fields. Zbl 0805.14028Shparlinski, Igor E.; Tsfasman, Michael A.; Vladut, Serge G. 20 1992 On a ternary quadratic form over primes. Zbl 1243.11093Fouvry, Étienne; Shparlinski, Igor E. 19 2011 On the divisibility of Fermat quotients. Zbl 1223.11116Bourgain, Jean; Ford, Kevin; Konyagin, Sergei V.; Shparlinski, Igor E. 19 2010 The insecurity of the digital signature algorithm with partially known nonces. Zbl 1009.94011Nguyen, Phong Q.; Shparlinski, Igor E. 19 2002 On exponential sums and group generators for elliptic curves over finite fields. Zbl 1032.11034Kohel, David R.; Shparlinski, Igor E. 19 2000 Modular hyperbolas. Zbl 1272.11050Shparlinski, Igor E. 18 2012 On the distribution and lattice structure of nonlinear congruential pseudorandom numbers. Zbl 0942.11037Niederreiter, Harald; Shparlinski, Igor E. 18 1999 On congruences with products of variables from short intervals and applications. Zbl 1301.11041Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 17 2013 On the distribution of the power generator. Zbl 1029.11042Friedlander, John B.; Shparlinski, Igor E. 17 2001 On the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1011.11055Shparlinski, Igor E. 17 2000 The insecurity of the elliptic curve digital signature algorithm with partially known nonces. Zbl 1039.94008Nguyen, Phong Q.; Shparlinski, Igor E. 16 2003 Character sums over integers with restricted \(g\)-ary digits. Zbl 1026.11068Banks, William D.; Conflitti, Alessandro; Shparlinski, Igor E. 16 2002 Orders of Gauss periods in finite fields. Zbl 0931.11057von zur Gathen, Joachim; Shparlinski, Igor 16 1998 Prime numbers with Beatty sequences. Zbl 1167.11010Banks, William D.; Shparlinski, Igor E. 15 2009 Dynamical systems generated by rational functions. Zbl 1030.11072Niederreiter, Harald; Shparlinski, Igor E. 15 2003 Exponential sums and rational points on complete intersections. Zbl 0719.11086Shparlinskij, Igor E.; Skorobogatov, Alexej N. 15 1990 On the energy of some circulant graphs. Zbl 1083.05029Shparlinski, Igor 14 2006 On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. Zbl 1116.14307Hess, Florian; Shparlinski, Igor E. 14 2005 On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. Zbl 1068.11043Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru 14 2005 Predicting nonlinear pseudorandom number generators. Zbl 1136.11316Blackburn, Simon R.; Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E. 14 2005 Arithmetic properties of numbers with restricted digits. Zbl 1049.11003Banks, William D.; Shparlinski, Igor E. 14 2004 On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. Zbl 1063.65005Gutierrez, Jaime; Shparlinski, Igor E.; Winterhof, Arne 14 2003 Cancellations amongst Kloosterman sums. Zbl 1368.11092Shparlinski, Igor E.; Zhang, Tianping 13 2016 On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E. 13 2012 Character sums with Fermat quotients. Zbl 1273.11126Shparlinski, Igor E. 13 2011 Bounds of multiplicative character sums with Fermat quotients of primes. Zbl 1221.11004Shparlinski, Igor E. 13 2011 Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E. 13 2008 On the distribution of points on multidimensional modular hyperbolas. Zbl 1123.11026Shparlinski, Igor E. 13 2007 Certain exponential sums and random walks on elliptic curves. Zbl 1068.11078Lange, Tanja; Shparlinski, Igor E. 13 2005 Predicting the inversive generator. Zbl 1123.94330Blackburn, Simon R.; Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E. 13 2003 On Gaussian sums for finite fields and elliptic curves. Zbl 0846.11064Shparlinski, I. E. 13 1992 Piatetski-Shapiro sequences. Zbl 1327.11062Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J. 12 2013 On the value set of Fermat quotients. Zbl 1305.11003Shparlinski, Igor E. 12 2012 On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. Zbl 1227.11093Ostafe, Alina; Shparlinski, Igor E. 12 2010 Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average. Zbl 1225.11101Shparlinski, Igor E. 12 2008 Character sums and congruences with \(n!\). Zbl 1060.11046Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 12 2004 Exponential sums over Mersenne numbers. Zbl 1060.11045Banks, William D.; Conflitti, Alessandro; Friedlander, John B.; Shparlinski, Igor E. 12 2004 On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504Shparlinski, Igor E.; Silverman, Joseph H. 12 2001 On the security of Diffie-Hellman bits. Zbl 0997.94548González Vasco, Maria Isabel; Shparlinski, Igor E. 12 2001 On the distribution of pseudorandom numbers and vectors generated by inversive methods. Zbl 0999.11040Niederreiter, Harald; Shparlinski, Igor E. 12 2000 Number theoretic methods in cryptography. Complexity lower bounds. Zbl 0912.11057Shparlinski, Igor 12 1999 Multiplicative congruences with variables from short intervals. Zbl 1385.11002Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 11 2014 On the consecutive powers of a primitive root: gaps and exponential sums. Zbl 1276.11005Konyagin, Sergei V.; Shparlinski, Igor E. 11 2012 Fermat quotients: exponential sums, value set and primitive roots. Zbl 1250.11005Shparlinski, Igor E. 11 2011 Multiplicative order of Gauss periods. Zbl 1201.11110Ahmadi, Omran; Shparlinski, Igor E.; Voloch, José Felipe 11 2010 On the concentration of points on modular hyperbolas and exponential curves. Zbl 1198.11002Chan, Tsz Ho; Shparlinski, Igor E. 11 2010 On the maximal difference between an element and its inverse in residue rings. Zbl 1131.11005Ford, Kevin; Khan, Mizan R.; Shparlinski, Igor E.; Yankov, Christian L. 11 2005 Some doubly exponential sums over \({\mathbb Z}_m\). Zbl 1018.11041Friedlander, John B.; Konyagin, Sergei; Shparlinski, Igor E. 11 2002 On finding primitive roots in finite fields. Zbl 0871.11091Shparlinski, Igor 11 1996 Prescribing the binary digits of squarefree numbers and quadratic residues. Zbl 1431.11015Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E. 10 2017 Points on curves in small boxes and applications. Zbl 1316.11024Chang, Mei-Chu; Cilleruelo, Javier; Garaev, Moubariz Z.; Hernández, José; Shparlinski, Igor E.; Zumalacárregui, Ana 10 2014 Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Zbl 1312.94048Farashahi, Reza R.; Fouque, Pierre-Alain; Shparlinski, Igor E.; Tibouchi, Mehdi; Voloch, J. Felipe 10 2013 On group structures realized by elliptic curves over arbitrary finite fields. Zbl 1257.11060Banks, William D.; Pappalardi, Francesco; Shparlinski, Igor E. 10 2012 On a generalisation of a Lehmer problem. Zbl 1269.11068Shparlinski, Igor E. 10 2009 Products in residue classes. Zbl 1182.11046Friedlander, John B.; Kurlberg, Pär; Shparlinski, Igor E. 10 2008 Distribution of some sequences of points on elliptic curves. Zbl 1129.14040Lange, Tanja; Shparlinski, Igor E. 10 2007 On values taken by the largest prime factor of shifted primes. Zbl 1139.11038Banks, William D.; Shparlinski, Igor E. 10 2007 On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states. Zbl 1110.81028Klappenecker, Andreas; Rötteler, Martin; Shparlinski, Igor E.; Winterhof, Arne 10 2005 Prime divisors of sparse integers. Zbl 1049.11010Shparlinski, I. E. 10 2003 On the maximal difference between an element and its inverse modulo \(n\). Zbl 1047.11003Khan, M. R.; Shparlinski, I. E. 10 2003 On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. Zbl 0958.11052Griffin, Frances; Niederreiter, Harald; Shparlinski, Igor E. 10 1999 Functional graphs of polynomials over finite fields. Zbl 1327.05323Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E. 9 2016 Isomorphism classes of elliptic curves over a finite field in some thin families. Zbl 1285.11092Cilleruelo, Javier; Shparlinski, Igor E.; Zumalacárregui, Ana 9 2012 On the number of solutions of exponential congruences. Zbl 1268.11048Balog, Antal; Broughan, Kevin A.; Shparlinski, Igor E. 9 2011 On the length of critical orbits of stable quadratic polynomials. Zbl 1268.11155Ostafe, Alina; Shparlinski, Igor E. 9 2010 On the solvability of bilinear equations in finite fields. Zbl 1246.11183Shparlinski, Igor E. 9 2008 Distribution of matrices with restricted entries over finite fields. Zbl 1181.11030Ahmadi, Omran; Shparlinski, Igor E. 9 2007 On some dynamical systems in finite fields and residue rings. Zbl 1127.11052Shparlinski, Igor E. 9 2007 Double character sums over elliptic curves and finite fields. Zbl 1171.11046Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E. 9 2006 On the lower bound of the linear complexity over \(\mathbb F_p\) of Sidelnikov sequences. Zbl 1296.94073Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor; Winterhof, Arne 9 2006 On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041Luca, Florian; Shparlinski, Igor E. 9 2005 Smooth orders and cryptographic applications. Zbl 1058.11059Pomerance, Carl; Shparlinski, Igor E. 9 2002 On the spectral Ádám property for circulant graphs. Zbl 1035.05059Mans, Bernard; Pappalardi, Francesco; Shparlinski, Igor 9 2002 On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period. Zbl 1011.11053Gutierrez, Jaime; Niederreiter, Harald; Shparlinski, Igor E. 9 2000 On certain exponential sums and the distribution of Diffie-Hellman triples. Zbl 0935.11028Canetti, Ran; Friedlander, John; Shparlinski, Igor 9 1999 Counting curves and their projections. Zbl 0990.68642von zur Gathen, Joachim; Karpinski, Marek; Shparlinski, Igor 9 1997 On the number of various prime divisors of recurrence sequence. Zbl 0635.10006Shparlinskiĭ, I. E. 9 1987 Divisor problem in arithmetic progressions modulo a prime power. Zbl 1436.11103Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping 8 2018 On the number of distinct elliptic curves in some families. Zbl 1269.11060Farashahi, Reza Rezaeian; Shparlinski, Igor E. 8 2010 Pseudorandom number generators from elliptic curves. Zbl 1246.11135Shparlinski, Igor E. 8 2009 Arithmetic functions on Beatty sequences. Zbl 1227.11045Abercrombie, Alex G.; Banks, William D.; Shparlinski, Igor E. 8 2009 Congruences with intervals and arbitrary sets. Zbl 07191876Banks, William; Shparlinski, Igor 2 2020 On large values of Weyl sums. Zbl 1447.11086Chen, Changhao; Shparlinski, Igor E. 1 2020 Kloosterman paths of prime powers moduli. II. Zbl 1456.11233Ricotta, Guillaume; Royer, Emmanuel; Shparlinski, Igor 1 2020 Sums of algebraic trace functions twisted by arithmetic functions. Zbl 07179068Korolev, Maxim; Shparlinski, Igor 1 2020 On the complexity of exact counting of dynamically irreducible polynomials. Zbl 07151949Gómez-Pérez, Domingo; Mérai, László; Shparlinski, Igor E. 1 2020 Unlikely intersections over finite fields: polynomial orbits in small subgroups. Zbl 07147532Mérai, László; Shparlinski, Igor E. 1 2020 Distribution of short subsequences of inversive congruential pseudorandom numbers modulo \(2^t\). Zbl 1439.11186Mérai, László; Shparlinski, Igor E. 1 2020 On sums of Kloosterman and Gauss sums. Zbl 1453.11105Shparlinski, Igor E. 7 2019 Cancellations between Kloosterman sums modulo a prime power with prime arguments. Zbl 1441.11192Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping 4 2019 Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems. Zbl 1403.37101D’Andrea, Carlos; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín 4 2019 On a sum involving the Euler function. Zbl 1454.11009Bordellès, Olivier; Dai, Lixia; Heyman, Randell; Pan, Hao; Shparlinski, Igor E. 3 2019 Bounds of trilinear and quadrilinear exponential sums. Zbl 1454.11151Petridis, Giorgis; Shparlinski, Igor E. 2 2019 On short products of primes in arithmetic progressions. Zbl 1456.11179Shparlinski, Igor E. 2 2019 Double sums of Kloosterman sums in finite fields. Zbl 1447.11117Macourt, Simon; Shparlinski, Igor E. 1 2019 Disjointness of the Möbius transformation and Möbius function. Zbl 1454.11147El Abdalaoui, El Houcein; Shparlinski, Igor E. 1 2019 On functional graphs of quadratic polynomials. Zbl 1417.05088Mans, Bernard; Sha, Min; Shparlinski, Igor E.; Sutantyo, Daniel 1 2019 On multiplicative dependence of values of rational functions and a generalization of the Northcott theorem. Zbl 1442.11142Ostafe, Alina; Sha, Min; Shparlinski, Igor E.; Zannier, Umberto 1 2019 Analogues of the Balog-Wooley decomposition for subsets of finite fields and character sums with convolutions. Zbl 07066612Roche-Newton, Oliver; Shparlinski, Igor E.; Winterhof, Arne 1 2019 On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E. 1 2019 Divisor problem in arithmetic progressions modulo a prime power. Zbl 1436.11103Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping 8 2018 Multiplicative energy of shifted subgroups and bounds on exponential sums with trinomials in finite fields. Zbl 1448.11213Macourt, Simon; Shkredov, Ilya D.; Shparlinski, Igor E. 3 2018 On multiplicatively dependent vectors of algebraic numbers. Zbl 1442.11134Pappalardi, Francesco; Sha, Min; Shparlinski, Igor E.; Stewart, Cameron L. 3 2018 Orbits of polynomial dynamical systems modulo primes. Zbl 1416.37081Chang, Mei-Chu; D’Andrea, Carlos; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín 3 2018 The Sato-Tate distribution in thin parametric families of elliptic curves. Zbl 1426.11057de la Bretèche, Régis; Sha, Min; Shparlinski, Igor E.; Voloch, José Felipe 2 2018 Linear equations with rational fractions of bounded height and stochastic matrices. Zbl 1422.11069Shparlinski, Igor E. 2 2018 Multiplicative orders in orbits of polynomials over finite fields. Zbl 1431.11130Shparlinski, Igor E. 2 2018 Polynomial interpolation and identity testing from high powers over finite fields. Zbl 1390.11128Ivanyos, Gábor; Karpinski, Marek; Santha, Miklos; Saxena, Nitin; Shparlinski, Igor E. 2 2018 Bilinear forms with exponential sums with binomials. Zbl 1429.11069Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping 2 2018 Double character sums with intervals and arbitrary sets. Zbl 07070257Shkredov, Ilya D.; Shparlinski, Igor E. 1 2018 On abelian multiplicatively dependent points on a curve in a torus. Zbl 1440.11101Ostafe, Alina; Sha, Min; Shparlinski, Igor E.; Zannier, Umberto 1 2018 Trilinear forms with double Kloosterman sums. Zbl 1447.11089Shparlinski, Igor E. 1 2018 Denominators of Bernoulli polynomials. Zbl 1415.11121Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. 1 2018 Elliptic curves in isogeny classes. Zbl 1444.11122Shparlinski, Igor E.; Zhao, Liangyi 1 2018 On the error term of a lattice counting problem. Zbl 1380.11085Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E. 1 2018 Prescribing the binary digits of squarefree numbers and quadratic residues. Zbl 1431.11015Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E. 10 2017 Orbits of algebraic dynamical systems in subgroups and subfields. Zbl 1393.37113Ostafe, Alina; Shparlinski, Igor E. 4 2017 Double exponential sums with exponential functions. Zbl 1428.11143Shparlinski, Igor E.; Yau, Kam Hung 3 2017 On some multiple character sums. Zbl 1427.11078Shkredov, Ilya D.; Shparlinski, Igor E. 3 2017 On distances in lattices from algebraic number fields. Zbl 1433.11083Dubickas, Artūras; Sha, Min; Shparlinski, Igor E. 2 2017 Squares in Piatetski-Shapiro sequences. Zbl 1428.11051Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping 2 2017 Power series approximations to Fekete polynomials. Zbl 1427.11030Bell, Jason; Shparlinski, Igor E. 2 2017 The Sato-Tate distribution in families of elliptic curves with a rational parameter of bounded height. Zbl 1410.11054Sha, Min; Shparlinski, Igor E. 2 2017 On two functions arising in the study of the Euler and Carmichael quotients. Zbl 1425.11009Luca, Florian; Sha, Min; Shparlinski, Igor E. 1 2017 Cancellations amongst Kloosterman sums. Zbl 1368.11092Shparlinski, Igor E.; Zhang, Tianping 13 2016 Functional graphs of polynomials over finite fields. Zbl 1327.05323Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E. 9 2016 Products of small integers in residue classes and additive properties of Fermat quotients. Zbl 1414.11109Harman, Glyn; Shparlinski, Igor E. 6 2016 Bounds of double multiplicative character sums and gaps between residues of exponential functions. Zbl 1419.11004Shparlinski, Igor E.; Yau, Kam-hung 4 2016 Polynomial values in small subgroups of finite fields. Zbl 1407.11051Shparlinski, Igor E. 3 2016 Linear congruences with ratios. Zbl 1383.11041Shparlinski, Igor E. 3 2016 Almost primes of the form \(\lfloor p^c \rfloor\). Zbl 1355.11099Banks, William D.; Guo, Victor Z.; Shparlinski, Igor E. 3 2016 Upper and lower bounds for higher moments of theta functions. Zbl 1409.11034Munsch, Marc; Shparlinski, Igor E. 3 2016 Groups generated by iterations of polynomials over finite fields. Zbl 1347.11084Shparlinski, Igor E. 3 2016 On the additive energy of the distance set in finite fields. Zbl 1403.11078Shparlinski, Igor E. 2 2016 Counting co-cyclic lattices. Zbl 1348.11056Nguyen, Phong Q.; Shparlinski, Igor E. 2 2016 On small gaps between the elements of multiplicative subgroups of finite fields. Zbl 1367.11040Shparlinski, Igor E. 2 2016 Cyclotomic coefficients: gaps and jumps. Zbl 1405.11032Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. 2 2016 On bilinear exponential and character sums with reciprocals of polynomials. Zbl 1400.11123Shparlinski, Igor E. 1 2016 Dynamical systems of non-algebraic origin: fixed points and orbit lengths. Zbl 1420.37119Shparlinski, Igor E. 1 2016 Ratios of small integers in multiplicative subgroups of residue rings. Zbl 1403.11062Shparlinski, Igor E. 1 2016 Fractional parts of Dedekind sums. Zbl 1419.11072Banks, William D.; Shparlinski, Igor E. 1 2016 Averaging operators over homogeneous varieties over finite fields. Zbl 1346.43002Koh, Doowon; Shen, Chun-Yen; Shparlinski, Igor 1 2016 On the density of integer points on generalised Markoff-Hurwitz and Dwork hypersurfaces. Zbl 1403.11026Chang, Mei-Chu; Shparlinski, Igor E. 1 2016 Counting irreducible binomials over finite fields. Zbl 1371.11150Heyman, Randell; Shparlinski, Igor E. 1 2016 Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 5 2015 On the fixed points of the map \(x \mapsto x^x\) modulo a prime. Zbl 1393.11029Kurlberg, Pär; Luca, Florian; Shparlinski, Igor E. 5 2015 Subgroups generated by rational functions in finite fields. Zbl 1395.11071Gómez-Pérez, Domingo; Shparlinski, Igor E. 5 2015 Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves. Zbl 1384.11033Sha, Min; Shparlinski, Igor E. 4 2015 Polynomial values in subfields and affine subspaces of finite fields. Zbl 1396.11016Roche-Newton, Oliver; Shparlinski, Igor E. 4 2015 Congruences with intervals and subgroups modulo a prime. Zbl 1379.11004Munsch, Marc; Shparlinski, Igor E. 3 2015 Quadratic non-residues in short intervals. Zbl 1378.11012Konyagin, Sergei V.; Shparlinski, Igor E. 3 2015 Explicit form of Cassels’ \(p\)-adic embedding theorem for number fields. Zbl 1326.11062Dubickas, Arturas; Sha, Min; Shparlinski, Igor 2 2015 On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average. Zbl 1400.11164Shparlinski, Igor E.; Sutherland, Andrew V. 2 2015 Cayley graphs generated by small degree polynomials over finite fields. Zbl 1311.05083Shparlinski, Igor E. 2 2015 Counting additive decompositions of quadratic residues in finite fields. Zbl 1393.11006Blackburn, Simon R.; Konyagin, Sergei V.; Shparlinski, Igor E. 1 2015 Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Zbl 1369.11100Shparlinski, Igor E. 1 2015 On the product of small Elkies primes. Zbl 1317.11061Shparlinski, Igor E. 1 2015 Multiplicative congruences with variables from short intervals. Zbl 1385.11002Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 11 2014 Points on curves in small boxes and applications. Zbl 1316.11024Chang, Mei-Chu; Cilleruelo, Javier; Garaev, Moubariz Z.; Hernández, José; Shparlinski, Igor E.; Zumalacárregui, Ana 10 2014 On irreducible divisors of iterated polynomials. Zbl 1339.11099Gómez-Pérez, Domingo; Ostafe, Alina; Shparlinski, Igor E. 5 2014 Double character sums over subgroups and intervals. Zbl 1316.11076Chang, Mei-Chu; Shparlinski, Igor E. 5 2014 On the distribution of Atkin and Elkies primes. Zbl 1312.11048Shparlinski, Igor E.; Sutherland, Andrew V. 5 2014 Elements of large order on varieties over prime finite fields. Zbl 1366.11084Chang, Mei-Chu; Kerr, Bryce; Shparlinski, Igor E.; Zannier, Umberto 4 2014 Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields. Zbl 1373.11081Shparlinski, Igor E. 4 2014 On shifted Eisenstein polynomials. Zbl 1340.11030Heyman, Randell; Shparlinski, Igor E. 3 2014 On the multidimensional distribution of the Naor-Reingold pseudo-random function. Zbl 1315.11067Ling, San; Shparlinski, Igor; Wang, Huaxiong 3 2014 On the counting function of elliptic Carmichael numbers. Zbl 1331.11115Luca, Florian; Shparlinski, Igor E. 3 2014 Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators. Zbl 1294.11131Gómez-Pérez, Domingo; Ostafe, Alina; Shparlinski, Igor 3 2014 Covering sets for limited-magnitude errors. Zbl 1360.11026Chen, Zhixiong; Shparlinski, Igor E.; Winterhof, Arne 2 2014 On the distribution of points on the generalized Markoff-Hurwitz and Dwork hypersurfaces. Zbl 1329.11026Shparlinski, Igor E. 2 2014 Periodic structure of the exponential pseudorandom number generator. Zbl 1368.11085Kaszián, Jonas; Moree, Pieter; Shparlinski, Igor E. 1 2014 Interpolation and approximation of polynomials in finite fields over a short interval from noisy values. Zbl 1310.11117Garcia-Morchon, Oscar; Rietman, Ronald; Shparlinski, Igor E.; Tolhuizen, Ludo 1 2014 Random walks, bisections and gossiping in circulant graphs. Zbl 1306.05227Mans, Bernard; Shparlinski, Igor 1 2014 Generators of elliptic curves over finite fields. Zbl 1316.11055Shparlinski, Igor E.; Voloch, José Felipe 1 2014 Distribution of exponential functions modulo a prime power. Zbl 1356.11002Shparlinski, Igor E. 1 2014 Multiple exponential and character sums with monomials. Zbl 1304.11083Shparlinski, Igor E. 1 2014 Squarefree parts of discriminants of trinomials. Zbl 1316.11083Shparlinski, Igor E. 1 2014 Distribution of elliptic twin primes in isogeny and isomorphism classes. Zbl 1317.11097Shparlinski, Igor E.; Sutantyo, Daniel 1 2014 On congruences with products of variables from short intervals and applications. Zbl 1301.11041Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 17 2013 Piatetski-Shapiro sequences. Zbl 1327.11062Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J. 12 2013 Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Zbl 1312.94048Farashahi, Reza R.; Fouque, Pierre-Alain; Shparlinski, Igor E.; Tibouchi, Mehdi; Voloch, J. Felipe 10 2013 ...and 418 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,351 Authors 275 Shparlinski, Igor E. 68 Luca, Florian 52 Winterhof, Arne 26 Garaev, Moubariz Z. 25 Ostafe, Alina 22 Banks, William D. 20 Shkredov, Il’ya Dmitrievich 19 Sha, Min 17 Chen, Zhixiong 16 Bourgain, Jean 16 Chang, Mei-Chu 15 Gomez-Perez, Domingo 15 von zur Gathen, Joachim 14 Cilleruelo, Javier 14 Konyagin, Sergeĭ Vladimirovich 14 Niederreiter, Harald 13 Meidl, Wilfried 13 Mérai, László 12 Ahmadi, Omran 12 Ballet, Stéphane 12 Panario, Daniel 12 Vinh, Le Anh 11 Bell, Jason P. 11 Dubickas, Artūras 11 Koh, Doowon 11 Korolëv, Maksim Aleksandrovich 11 Sanna, Carlo 10 Gutierrez, Jaime 9 Bašić, Milan 9 Farashahi, Reza Rezaeian 9 Friedlander, John Benjamin 9 Zaharescu, Alexandru 8 Gómez, Domingo 8 Munsch, Marc 7 Cochrane, Todd 7 Ford, Kevin B. 7 Ilić, Aleksandar 7 Kerr, Bryce 7 Pollack, Paul 7 Wan, Daqing 7 Zhang, Tianping 6 Baier, Stephan 6 Blake, Ian F. 6 Cojocaru, Alina Carmen 6 Du, Xiaoni 6 Galbraith, Steven D. 6 Gao, Shuhong 6 Micheli, Giacomo 6 Moree, Pieter 6 Pappalardi, Francesco 6 Pham Van Thang 6 Shen, Chun-Yen 6 Tibouchi, Mehdi 6 Voloch, José Felipe 6 Zhang, Wenpeng 5 Aly, Hassan Y. 5 Cao, Xiwang 5 Cheng, Qi 5 Cohen, Stephen D. 5 Dartyge, Cécile 5 El-Mahassni, Edwin D. 5 García, Victor Cuauhtemoc 5 Harvey, David I. 5 Ibeas, Álvar 5 Karpinski, Marek 5 Lange, Tanja 5 Macourt, Simon 5 Mauduit, Christian 5 Mefenza, Thierry 5 Mkaouar, Mohamed 5 Murty, Maruti Ram 5 Reis, Lucas 5 Sander, Jürgen W. 5 Sárközy, András 5 Shani, Barak 5 Shteĭnikov, Yuriĭ Nikolaevich 5 Topuzoǧlu, Alev 5 Wu, Chenhuang 5 Yau, Kam-hung 5 Zumalacárregui, Ana 4 Blackburn, Simon R. 4 Dietmann, Rainer 4 Elsholtz, Christian 4 Garefalakis, Theo 4 Garton, Derek 4 Goryashin, Dmitriĭ Viktorovich 4 Grau, José María 4 Grigor’ev, Dmitriĭ Yur’evich 4 Heyman, Randell 4 Hu, Lei 4 Jiménez-Urroz, Jorge 4 Jones, Lenny K. 4 Jones, Rafe 4 Knopfmacher, Arnold 4 Leedham-Green, Charles R. 4 Li, Jiyou 4 Mak, Kit-Ho 4 Mans, Bernard 4 Meletiou, Gerasimos C. 4 Mokhtar, Hamid ...and 1,251 more Authors all top 5 Cited in 201 Serials 121 Journal of Number Theory 89 Finite Fields and their Applications 52 Designs, Codes and Cryptography 49 International Journal of Number Theory 47 Mathematics of Computation 43 Proceedings of the American Mathematical Society 38 Bulletin of the Australian Mathematical Society 28 Journal of Symbolic Computation 28 Linear Algebra and its Applications 27 Information Processing Letters 26 Monatshefte für Mathematik 24 Mathematical Notes 23 Acta Arithmetica 22 Theoretical Computer Science 21 Applicable Algebra in Engineering, Communication and Computing 20 Discrete Applied Mathematics 18 Indagationes Mathematicae. New Series 17 Transactions of the American Mathematical Society 17 Journal of Complexity 16 Periodica Mathematica Hungarica 15 Mathematika 15 Journal de Théorie des Nombres de Bordeaux 14 Israel Journal of Mathematics 14 Proceedings of the Steklov Institute of Mathematics 12 Integers 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Journal of Mathematical Cryptology 11 Journal of Algebra 11 Mathematische Zeitschrift 11 Experimental Mathematics 11 The Ramanujan Journal 10 Archiv der Mathematik 10 Functiones et Approximatio. Commentarii Mathematici 10 Advances in Mathematics of Communications 9 Discrete Mathematics 9 Cryptography and Communications 8 Rocky Mountain Journal of Mathematics 8 Acta Mathematica Sinica. 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Mathematics 5 Research in Number Theory 4 Indian Journal of Pure & Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Lithuanian Mathematical Journal 4 Inventiones Mathematicae 4 Journal of Combinatorial Theory. Series A 4 Journal of Pure and Applied Algebra 4 European Journal of Combinatorics 4 Journal of Cryptology 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annals of Combinatorics 4 Research in the Mathematical Sciences 3 Computers & Mathematics with Applications 3 Czechoslovak Mathematical Journal 3 Duke Mathematical Journal 3 Journal of Computer and System Sciences 3 Manuscripta Mathematica 3 Pacific Journal of Mathematics 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Quaestiones Mathematicae 3 The Journal of Fourier Analysis and Applications 3 Journal of Inequalities and Applications 3 Journal of Discrete Mathematical Sciences & Cryptography 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Systems Science and Complexity 3 International Journal of Quantum Information 3 Science China. Information Sciences 3 Forum of Mathematics, Sigma 2 Problems of Information Transmission 2 Ukrainian Mathematical Journal 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Bulletin of the London Mathematical Society 2 Canadian Journal of Mathematics 2 Information Sciences 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Approximation Theory 2 Journal of Functional Analysis 2 Matematički Vesnik ...and 101 more Serials all top 5 Cited in 44 Fields 1,077 Number theory (11-XX) 235 Information and communication theory, circuits (94-XX) 140 Combinatorics (05-XX) 134 Computer science (68-XX) 102 Algebraic geometry (14-XX) 59 Dynamical systems and ergodic theory (37-XX) 54 Numerical analysis (65-XX) 42 Field theory and polynomials (12-XX) 40 Group theory and generalizations (20-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 27 Quantum theory (81-XX) 26 Commutative algebra (13-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 13 Probability theory and stochastic processes (60-XX) 11 Convex and discrete geometry (52-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 8 Functions of a complex variable (30-XX) 8 Functional analysis (46-XX) 6 Associative rings and algebras (16-XX) 6 Special functions (33-XX) 6 Abstract harmonic analysis (43-XX) 5 Mathematical logic and foundations (03-XX) 5 Real functions (26-XX) 5 Geometry (51-XX) 4 Nonassociative rings and algebras (17-XX) 4 Topological groups, Lie groups (22-XX) 4 Approximations and expansions (41-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Operations research, mathematical programming (90-XX) 4 Biology and other natural sciences (92-XX) 3 History and biography (01-XX) 3 Measure and integration (28-XX) 3 Sequences, series, summability (40-XX) 3 Operator theory (47-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Partial differential equations (35-XX) 2 Difference and functional equations (39-XX) 1 Category theory; homological algebra (18-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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