Mérai, László; Shparlinski, Igor E. Distribution of recursive matrix pseudorandom number generator modulo prime powers. (English) Zbl 07810336 Math. Comput. 93, No. 347, 1355-1370 (2024). MSC: 11K38 11K45 11L07 PDFBibTeX XMLCite \textit{L. Mérai} and \textit{I. E. Shparlinski}, Math. Comput. 93, No. 347, 1355--1370 (2024; Zbl 07810336) Full Text: DOI arXiv
Shkredov, Ilya D.; Shparlinski, Igor E.; Zaharescu, Alexandru On the distribution of modular square roots of primes. (English) Zbl 07807524 Math. Z. 306, No. 3, Paper No. 43, 17 p. (2024). MSC: 11K38 11L07 11L20 PDFBibTeX XMLCite \textit{I. D. Shkredov} et al., Math. Z. 306, No. 3, Paper No. 43, 17 p. (2024; Zbl 07807524) Full Text: DOI arXiv OA License
Ostafe, Alina; Shparlinski, Igor E.; Voloch, José Felipe Weil sums over small subgroups. (English) Zbl 07783182 Math. Proc. Camb. Philos. Soc. 176, No. 1, 39-53 (2024). MSC: 11T23 11D79 11L07 PDFBibTeX XMLCite \textit{A. Ostafe} et al., Math. Proc. Camb. Philos. Soc. 176, No. 1, 39--53 (2024; Zbl 07783182) Full Text: DOI arXiv
Mans, Bernard; Sha, Min; Shparlinski, Igor E.; Sutantyo, Daniel Functional graphs of families of quadratic polynomials. (English) Zbl 07689732 Math. Comput. 92, No. 343, 2307-2331 (2023). MSC: 11T06 11T24 11G20 05C25 05C69 PDFBibTeX XMLCite \textit{B. Mans} et al., Math. Comput. 92, No. 343, 2307--2331 (2023; Zbl 07689732) Full Text: DOI arXiv
Ostafe, Alina; Shparlinski, Igor E. On the Skolem problem and some related questions for parametric families of linear recurrence sequences. (English) Zbl 1498.11046 Can. J. Math. 74, No. 3, 773-792 (2022). Reviewer: Clemens Fuchs (Salzburg) MSC: 11B37 11D61 PDFBibTeX XMLCite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Can. J. Math. 74, No. 3, 773--792 (2022; Zbl 1498.11046) Full Text: DOI arXiv
Mérai, László; Ostafe, Alina; Shparlinski, Igor E. Dynamical irreducibility of polynomials modulo primes. (English) Zbl 1489.11177 Math. Z. 298, No. 3-4, 1187-1199 (2021). Reviewer: Artūras Dubickas (Vilnius) MSC: 11R06 11N36 37P05 PDFBibTeX XMLCite \textit{L. Mérai} et al., Math. Z. 298, No. 3--4, 1187--1199 (2021; Zbl 1489.11177) Full Text: DOI arXiv
Shparlinski, Igor E.; Wang, Qiang Exponential sums with sparse polynomials over finite fields. (English) Zbl 1469.11274 SIAM J. Discrete Math. 35, No. 2, 976-987 (2021). MSC: 11L07 11T23 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{Q. Wang}, SIAM J. Discrete Math. 35, No. 2, 976--987 (2021; Zbl 1469.11274) Full Text: DOI arXiv
Mérai, László; Shparlinski, Igor E. On the dynamical system generated by the Möbius transformation at prime times. (English) Zbl 1481.11082 Res. Math. Sci. 8, No. 1, Paper No. 10, 13 p. (2021). Reviewer: Huaning Liu (Xi’an) MSC: 11L07 11N60 11T23 37P05 PDFBibTeX XMLCite \textit{L. Mérai} and \textit{I. E. Shparlinski}, Res. Math. Sci. 8, No. 1, Paper No. 10, 13 p. (2021; Zbl 1481.11082) Full Text: DOI arXiv
Dunn, Alexander; Kerr, Bryce; Shparlinski, Igor E.; Zaharescu, Alexandru Bilinear forms in Weyl sums for modular square roots and applications. (English) Zbl 1469.11270 Adv. Math. 375, Article ID 107369, 58 p. (2020). MSC: 11L07 11E25 11K38 11L20 11N32 PDFBibTeX XMLCite \textit{A. Dunn} et al., Adv. Math. 375, Article ID 107369, 58 p. (2020; Zbl 1469.11270) Full Text: DOI arXiv
Munsch, Marc; Shparlinski, Igor E. On smooth square-free numbers in arithmetic progressions. (English) Zbl 1469.11375 J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041-1067 (2020). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11B25 11L40 PDFBibTeX XMLCite \textit{M. Munsch} and \textit{I. E. Shparlinski}, J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041--1067 (2020; Zbl 1469.11375) Full Text: DOI arXiv
Mérai, László; Shparlinski, Igor E. Unlikely intersections over finite fields: polynomial orbits in small subgroups. (English) Zbl 1489.11201 Discrete Contin. Dyn. Syst. 40, No. 2, 1065-1073 (2020). MSC: 11T06 11D79 37P05 37P25 PDFBibTeX XMLCite \textit{L. Mérai} and \textit{I. E. Shparlinski}, Discrete Contin. Dyn. Syst. 40, No. 2, 1065--1073 (2020; Zbl 1489.11201) Full Text: DOI arXiv
Mérai, László; Shparlinski, Igor E. Distribution of short subsequences of inversive congruential pseudorandom numbers modulo \(2^t\). (English) Zbl 1439.11186 Math. Comput. 89, No. 322, 911-922 (2020). Reviewer: Arne Winterhof (Linz) MSC: 11K38 11K45 11L07 PDFBibTeX XMLCite \textit{L. Mérai} and \textit{I. E. Shparlinski}, Math. Comput. 89, No. 322, 911--922 (2020; Zbl 1439.11186) Full Text: DOI arXiv
Roche-Newton, Oliver; Shparlinski, Igor E.; Winterhof, Arne Analogues of the Balog-Wooley decomposition for subsets of finite fields and character sums with convolutions. (English) Zbl 1473.11033 Ann. Comb. 23, No. 1, 183-205 (2019). MSC: 11B30 11T24 PDFBibTeX XMLCite \textit{O. Roche-Newton} et al., Ann. Comb. 23, No. 1, 183--205 (2019; Zbl 1473.11033) Full Text: DOI arXiv
Shparlinski, Igor E. The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields. (English) Zbl 1443.11102 Int. J. Number Theory 15, No. 3, 469-477 (2019). MSC: 11G05 11G20 11T30 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Int. J. Number Theory 15, No. 3, 469--477 (2019; Zbl 1443.11102) Full Text: DOI
Liu, Kui; Shparlinski, Igor E.; Zhang, Tianping Cancellations between Kloosterman sums modulo a prime power with prime arguments. (English) Zbl 1441.11192 Mathematika 65, No. 3, 475-487 (2019). MSC: 11L05 11T23 PDFBibTeX XMLCite \textit{K. Liu} et al., Mathematika 65, No. 3, 475--487 (2019; Zbl 1441.11192) Full Text: DOI arXiv
Shparlinski, Igor E. On short products of primes in arithmetic progressions. (English) Zbl 1456.11179 Proc. Am. Math. Soc. 147, No. 3, 977-986 (2019). MSC: 11N25 11B25 11L07 11N36 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 147, No. 3, 977--986 (2019; Zbl 1456.11179) Full Text: DOI arXiv
de la Bretèche, Régis; Sha, Min; Shparlinski, Igor E.; Voloch, José Felipe The Sato-Tate distribution in thin parametric families of elliptic curves. (English) Zbl 1426.11057 Math. Z. 290, No. 3-4, 831-855 (2018). Reviewer: Mohammad Sadek (New Cairo) MSC: 11G05 11G20 14H52 PDFBibTeX XMLCite \textit{R. de la Bretèche} et al., Math. Z. 290, No. 3--4, 831--855 (2018; Zbl 1426.11057) Full Text: DOI arXiv
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E. On the error term of a lattice counting problem. (English) Zbl 1380.11085 J. Number Theory 182, 19-36 (2018). Reviewer: Katherine Roegner (Berlin) MSC: 11H06 11K38 11P21 PDFBibTeX XMLCite \textit{O. Bordellès} et al., J. Number Theory 182, 19--36 (2018; Zbl 1380.11085) Full Text: DOI arXiv
Sha, Min; Shparlinski, Igor E. The Sato-Tate distribution in families of elliptic curves with a rational parameter of bounded height. (English) Zbl 1410.11054 Indag. Math., New Ser. 28, No. 2, 306-320 (2017). MSC: 11G05 11G50 14H52 PDFBibTeX XMLCite \textit{M. Sha} and \textit{I. E. Shparlinski}, Indag. Math., New Ser. 28, No. 2, 306--320 (2017; Zbl 1410.11054) Full Text: DOI arXiv
Shparlinski, Igor E.; Zhang, Tianping Cancellations amongst Kloosterman sums. (English) Zbl 1368.11092 Acta Arith. 176, No. 3, 201-210 (2016). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11L07 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{T. Zhang}, Acta Arith. 176, No. 3, 201--210 (2016; Zbl 1368.11092) Full Text: DOI arXiv
Banks, William D.; Shparlinski, Igor E. On Gauss sums and the evaluation of Stechkin’s constant. (English) Zbl 1339.11078 Math. Comput. 85, No. 301, 2569-2581 (2016). Reviewer: Huaning Liu (Shaanxi) MSC: 11L05 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, Math. Comput. 85, No. 301, 2569--2581 (2016; Zbl 1339.11078) Full Text: DOI arXiv
Banks, William D.; Shparlinski, Igor E. Fractional parts of Dedekind sums. (English) Zbl 1419.11072 Int. J. Number Theory 12, No. 5, 1137-1147 (2016). MSC: 11F20 11J71 11L05 11L40 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, Int. J. Number Theory 12, No. 5, 1137--1147 (2016; Zbl 1419.11072) Full Text: DOI arXiv
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. Cyclotomic coefficients: gaps and jumps. (English) Zbl 1405.11032 J. Number Theory 163, 211-237 (2016). MSC: 11C08 11B83 11L07 11N25 PDFBibTeX XMLCite \textit{O.-M. Camburu} et al., J. Number Theory 163, 211--237 (2016; Zbl 1405.11032) Full Text: DOI arXiv
Shparlinski, Igor E. Groups generated by iterations of polynomials over finite fields. (English) Zbl 1347.11084 Proc. Edinb. Math. Soc., II. Ser. 59, No. 1, 235-245 (2016). Reviewer: Florian Pausinger (Garching) MSC: 11T06 11T24 37P05 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Edinb. Math. Soc., II. Ser. 59, No. 1, 235--245 (2016; Zbl 1347.11084) Full Text: DOI
Shparlinski, Igor E. Distribution of polynomial discriminants modulo a prime. (English) Zbl 1364.11153 Arch. Math. 105, No. 3, 251-259 (2015). Reviewer: Astrid Reifegerste (Magdeburg) MSC: 11T06 11T23 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Arch. Math. 105, No. 3, 251--259 (2015; Zbl 1364.11153) Full Text: DOI
Sha, Min; Shparlinski, Igor E. Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves. (English) Zbl 1384.11033 Acta Arith. 170, No. 4, 299-325 (2015). Reviewer: Andrea Bandini (Parma) MSC: 11B57 11G05 11G20 14H52 PDFBibTeX XMLCite \textit{M. Sha} and \textit{I. E. Shparlinski}, Acta Arith. 170, No. 4, 299--325 (2015; Zbl 1384.11033) Full Text: DOI arXiv
Shparlinski, Igor E. Cayley graphs generated by small degree polynomials over finite fields. (English) Zbl 1311.05083 SIAM J. Discrete Math. 29, No. 1, 376-381 (2015). MSC: 05C25 05C50 11L10 11T06 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, SIAM J. Discrete Math. 29, No. 1, 376--381 (2015; Zbl 1311.05083) Full Text: DOI arXiv
Mans, Bernard; Shparlinski, Igor Random walks, bisections and gossiping in circulant graphs. (English) Zbl 1306.05227 Algorithmica 70, No. 2, 301-325 (2014). MSC: 05C81 05C80 05C85 05C25 PDFBibTeX XMLCite \textit{B. Mans} and \textit{I. Shparlinski}, Algorithmica 70, No. 2, 301--325 (2014; Zbl 1306.05227) Full Text: DOI
Ling, San; Shparlinski, Igor; Wang, Huaxiong On the multidimensional distribution of the Naor-Reingold pseudo-random function. (English) Zbl 1315.11067 Math. Comput. 83, No. 289, 2429-2434 (2014). Reviewer: Yaochen Zhu (Beijing) MSC: 11K45 11T23 65C10 94A60 PDFBibTeX XMLCite \textit{S. Ling} et al., Math. Comput. 83, No. 289, 2429--2434 (2014; Zbl 1315.11067) Full Text: DOI
Shparlinski, Igor E.; Sutherland, Andrew V. On the distribution of Atkin and Elkies primes. (English) Zbl 1312.11048 Found. Comput. Math. 14, No. 2, 285-297 (2014). Reviewer: Robert Fitzgerald (Carbondale) MSC: 11G07 11L40 11Y16 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{A. V. Sutherland}, Found. Comput. Math. 14, No. 2, 285--297 (2014; Zbl 1312.11048) Full Text: DOI arXiv
Gómez-Pérez, Domingo; Ostafe, Alina; Shparlinski, Igor Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators. (English) Zbl 1294.11131 Math. Comput. 83, No. 287, 1535-1550 (2014). Reviewer: Huaning Liu (Shaanxi) MSC: 11K45 37A45 11T71 65C10 94A60 PDFBibTeX XMLCite \textit{D. Gómez-Pérez} et al., Math. Comput. 83, No. 287, 1535--1550 (2014; Zbl 1294.11131) Full Text: DOI
Kerr, Bryce; Shparlinski, Igor E. On the distribution of values and zeros of polynomial systems over arbitrary sets. (English) Zbl 1297.11088 J. Number Theory 133, No. 9, 2863-2873 (2013). MSC: 11K38 11L07 11D79 PDFBibTeX XMLCite \textit{B. Kerr} and \textit{I. E. Shparlinski}, J. Number Theory 133, No. 9, 2863--2873 (2013; Zbl 1297.11088) Full Text: DOI arXiv
Shparlinski, Igor E. On products of primes and almost primes in arithmetic progressions. (English) Zbl 1299.11067 Period. Math. Hung. 67, No. 1, 55-61 (2013). Reviewer: Lajos Hajdu (Debrecen) MSC: 11N13 11L03 11N35 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Period. Math. Hung. 67, No. 1, 55--61 (2013; Zbl 1299.11067) Full Text: DOI
Shparlinski, Igor E. On the Sato-Tate conjecture on average for some families of elliptic curves. (English) Zbl 1325.11056 Forum Math. 25, No. 3, 647-664 (2013). MSC: 11G05 11L40 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Forum Math. 25, No. 3, 647--664 (2013; Zbl 1325.11056) Full Text: DOI
Gutierrez, Jaime; Ibeas, Álvar; Gómez-Pérez, Domingo; Shparlinski, Igor E. Predicting masked linear pseudorandom number generators over finite fields. (English) Zbl 1279.94082 Des. Codes Cryptography 67, No. 3, 395-402 (2013). MSC: 94A60 11T71 11K45 94A55 PDFBibTeX XMLCite \textit{J. Gutierrez} et al., Des. Codes Cryptography 67, No. 3, 395--402 (2013; Zbl 1279.94082) Full Text: DOI
Shparlinski, Igor E. Modular hyperbolas. (English) Zbl 1272.11050 Jpn. J. Math. (3) 7, No. 2, 235-294 (2012). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11D79 11-02 11L05 11L07 11L40 11N69 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Jpn. J. Math. (3) 7, No. 2, 235--294 (2012; Zbl 1272.11050) Full Text: DOI arXiv
Cilleruelo, Javier; Garaev, Moubariz Z.; Ostafe, Alina; Shparlinski, Igor E. On the concentration of points of polynomial maps and applications. (English) Zbl 1285.11027 Math. Z. 272, No. 3-4, 825-837 (2012). Reviewer: Enzo Bonacci (Latina) MSC: 11B50 37A45 11L07 11B30 37P05 PDFBibTeX XMLCite \textit{J. Cilleruelo} et al., Math. Z. 272, No. 3--4, 825--837 (2012; Zbl 1285.11027) Full Text: DOI
Ostafe, Alina; Shparlinski, Igor E. On the power generator and its multivariate analogue. (English) Zbl 1273.11118 J. Complexity 28, No. 2, 238-249 (2012). Reviewer: Yaochen Zhu (Beijing) MSC: 11K45 11L03 11K38 65C10 PDFBibTeX XMLCite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, J. Complexity 28, No. 2, 238--249 (2012; Zbl 1273.11118) Full Text: DOI
Ostafe, Alina; Shparlinski, Igor E.; Winterhof, Arne Multiplicative character sums of a class of nonlinear recurrence vector sequences. (English) Zbl 1247.11107 Int. J. Number Theory 7, No. 6, 1557-1571 (2011). Reviewer: Jebrel M. Habeb (Irbid) MSC: 11L40 11T06 11T24 PDFBibTeX XMLCite \textit{A. Ostafe} et al., Int. J. Number Theory 7, No. 6, 1557--1571 (2011; Zbl 1247.11107) Full Text: DOI
Shparlinski, Igor E. On the average distribution of pseudorandom numbers generated by nonlinear permutations. (English) Zbl 1219.11181 Math. Comput. 80, No. 274, 1053-1061 (2011). Reviewer: Arne Winterhof (Linz) MSC: 11T23 11K45 65C10 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Math. Comput. 80, No. 274, 1053--1061 (2011; Zbl 1219.11181) Full Text: DOI
Ostafe, Alina; Pelican, Elena; Shparlinski, Igor E. On pseudorandom numbers from multivariate polynomial systems. (English) Zbl 1254.11076 Finite Fields Appl. 16, No. 5, 320-328 (2010). Reviewer: Peter Kritzer (Linz) MSC: 11K45 11T23 37A45 37F10 PDFBibTeX XMLCite \textit{A. Ostafe} et al., Finite Fields Appl. 16, No. 5, 320--328 (2010; Zbl 1254.11076) Full Text: DOI
Ostafe, Alina; Shparlinski, Igor E. On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. (English) Zbl 1227.11093 Math. Comput. 79, No. 269, 501-511 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11K45 11T23 37A45 37F10 PDFBibTeX XMLCite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Math. Comput. 79, No. 269, 501--511 (2010; Zbl 1227.11093) Full Text: DOI arXiv
Iosevich, Alex; Shparlinski, Igor E.; Xiong, Maosheng Sets with integral distances in finite fields. (English) Zbl 1192.05020 Trans. Am. Math. Soc. 362, No. 4, 2189-2204 (2010). Reviewer: Gary L. Ebert (Newark/Delaware) MSC: 05B25 11T23 52C10 PDFBibTeX XMLCite \textit{A. Iosevich} et al., Trans. Am. Math. Soc. 362, No. 4, 2189--2204 (2010; Zbl 1192.05020) Full Text: DOI
Ostafe, Alina; Shparlinski, Igor E. Pseudorandom numbers and hash functions from iterations of multivariate polynomials. (English) Zbl 1185.11049 Cryptogr. Commun. 2, No. 1, 49-67 (2010). Reviewer: Arne Winterhof (Linz) MSC: 11K45 11T23 65C10 94A60 PDFBibTeX XMLCite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Cryptogr. Commun. 2, No. 1, 49--67 (2010; Zbl 1185.11049) Full Text: DOI arXiv
Farashahi, Reza Rezaeian; Shparlinski, Igor E. On the number of distinct elliptic curves in some families. (English) Zbl 1269.11060 Des. Codes Cryptography 54, No. 1, 83-99 (2010). MSC: 11G20 11G05 14G50 PDFBibTeX XMLCite \textit{R. R. Farashahi} and \textit{I. E. Shparlinski}, Des. Codes Cryptography 54, No. 1, 83--99 (2010; Zbl 1269.11060) Full Text: DOI
Shparlinski, Igor E. On quadratic fields generated by discriminants of irreducible trinomials. (English) Zbl 1218.11102 Proc. Am. Math. Soc. 138, No. 1, 125-132 (2010). MSC: 11R09 11R11 11L40 11N36 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 138, No. 1, 125--132 (2010; Zbl 1218.11102) Full Text: DOI arXiv
Banks, William D.; Shparlinski, Igor E. Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. (English) Zbl 1250.11064 Isr. J. Math. 173, 253-277 (2009). Reviewer: Thomas Ward (Bristol) MSC: 11G20 11L40 11T24 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, Isr. J. Math. 173, 253--277 (2009; Zbl 1250.11064) Full Text: DOI arXiv
Katz, Nicholas M.; Shparlinski, Igor E.; Xiong, Maosheng On character sums with distances on the upper half plane over a finite field. (English) Zbl 1253.11109 Finite Fields Appl. 15, No. 6, 738-747 (2009). Reviewer: Imin Chen (Burnaby) MSC: 11T24 11T60 PDFBibTeX XMLCite \textit{N. M. Katz} et al., Finite Fields Appl. 15, No. 6, 738--747 (2009; Zbl 1253.11109) Full Text: DOI
Shparlinski, Igor E. On a generalisation of a Lehmer problem. (English) Zbl 1269.11068 Math. Z. 263, No. 3, 619-631 (2009). MSC: 11K36 11L40 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Math. Z. 263, No. 3, 619--631 (2009; Zbl 1269.11068) Full Text: DOI arXiv
Balasuriya, Sanka; Shparlinski, Igor E.; Winterhof, Arne An average bound for character sums with some counter-dependent recurrence sequences. (English) Zbl 1181.11052 Rocky Mt. J. Math. 39, No. 5, 1403-1409 (2009). Reviewer: Florian Luca (Morelia) MSC: 11L07 11L40 PDFBibTeX XMLCite \textit{S. Balasuriya} et al., Rocky Mt. J. Math. 39, No. 5, 1403--1409 (2009; Zbl 1181.11052) Full Text: DOI
Shparlinski, Igor E.; Voloch, José Felipe Average distribution of prime ideals in families of number fields. (English) Zbl 1236.11098 Bull. Braz. Math. Soc. (N.S.) 39, No. 3, 417-425 (2008). Reviewer: Pieter Moree (Bonn) MSC: 11R44 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{J. F. Voloch}, Bull. Braz. Math. Soc. (N.S.) 39, No. 3, 417--425 (2008; Zbl 1236.11098) Full Text: DOI
Shparlinski, Igor On the size of the Jacobians of curves over finite fields. (English) Zbl 1183.11033 Bull. Braz. Math. Soc. (N.S.) 39, No. 4, 587-595 (2008). MSC: 11G20 11K38 14H40 PDFBibTeX XMLCite \textit{I. Shparlinski}, Bull. Braz. Math. Soc. (N.S.) 39, No. 4, 587--595 (2008; Zbl 1183.11033) Full Text: DOI
Shparlinski, Igor E. Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average. (English) Zbl 1225.11101 Mich. Math. J. 56, No. 1, 99-111 (2008). Reviewer: Tatyana L. Todorova (Sofia) MSC: 11L05 11A07 11A99 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Mich. Math. J. 56, No. 1, 99--111 (2008; Zbl 1225.11101) Full Text: DOI arXiv
van Dam, Wim; Shparlinski, Igor E. Classical and quantum algorithms for exponential congruences. (English) Zbl 1162.68829 Kawano, Yasuhito (ed.) et al., Theory of quantum computation, communication, and cryptography. Third workshop, TQC 2008, Tokyo, Japan, January 30–February 1, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-540-89303-5/pbk). Lecture Notes in Computer Science 5106, 1-10 (2008). MSC: 68W30 68Q25 81P68 PDFBibTeX XMLCite \textit{W. van Dam} and \textit{I. E. Shparlinski}, Lect. Notes Comput. Sci. 5106, 1--10 (2008; Zbl 1162.68829) Full Text: DOI arXiv
Shparlinski, Igor E.; Winterhof, Arne On the number of distances between the coordinates of points on modular hyperbolas. (English) Zbl 1137.11063 J. Number Theory 128, No. 5, 1224-1230 (2008). Reviewer: Pieter Moree (Bonn) MSC: 11N25 11A07 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{A. Winterhof}, J. Number Theory 128, No. 5, 1224--1230 (2008; Zbl 1137.11063) Full Text: DOI
Shparlinski, Igor Bilinear character sums over elliptic curves. (English) Zbl 1138.11035 Finite Fields Appl. 14, No. 1, 132-141 (2008). Reviewer: Zhefeng Xu (Xi’an) MSC: 11L40 11G05 PDFBibTeX XMLCite \textit{I. Shparlinski}, Finite Fields Appl. 14, No. 1, 132--141 (2008; Zbl 1138.11035) Full Text: DOI
Shparlinski, Igor E. On the distribution of Kloosterman sums. (English) Zbl 1157.11034 Proc. Am. Math. Soc. 136, No. 2, 419-425 (2008). Reviewer: Angel V. Kumchev (Towson) MSC: 11L05 11L40 11T71 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 136, No. 2, 419--425 (2008; Zbl 1157.11034) Full Text: DOI arXiv
Shparlinski, Igor E.; Winterhof, Arne Quantum period reconstruction of approximate sequences. (English) Zbl 1184.68259 Inf. Process. Lett. 103, No. 6, 211-215 (2007). MSC: 68Q12 PDFBibTeX XMLCite \textit{I. E. Shparlinski} and \textit{A. Winterhof}, Inf. Process. Lett. 103, No. 6, 211--215 (2007; Zbl 1184.68259) Full Text: DOI
Ahmadi, Omran; Shparlinski, Igor E. Distribution of matrices with restricted entries over finite fields. (English) Zbl 1181.11030 Indag. Math., New Ser. 18, No. 3, 327-337 (2007). MSC: 11C20 11D79 11T06 15B33 PDFBibTeX XMLCite \textit{O. Ahmadi} and \textit{I. E. Shparlinski}, Indag. Math., New Ser. 18, No. 3, 327--337 (2007; Zbl 1181.11030) Full Text: DOI
Shparlinski, Igor E. On the distribution of points on multidimensional modular hyperbolas. (English) Zbl 1123.11026 Proc. Japan Acad., Ser. A 83, No. 2, 5-9 (2007). Reviewer: Jürgen Spilker (Freiburg i. Br.) MSC: 11K38 11A07 11L40 11N37 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Japan Acad., Ser. A 83, No. 2, 5--9 (2007; Zbl 1123.11026) Full Text: DOI Euclid
Banks, William D.; Shparlinski, Igor E. Prime divisors in Beatty sequences. (English) Zbl 1198.11083 J. Number Theory 123, No. 2, 413-425 (2007). Reviewer: Florian Luca (Morelia) MSC: 11N64 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, J. Number Theory 123, No. 2, 413--425 (2007; Zbl 1198.11083) Full Text: DOI
Saxena, Nitin; Severini, Simone; Shparlinski, Igor E. Parameters of integral circulant graphs and periodic quantum dynamics. (English) Zbl 1119.81042 Int. J. Quantum Inf. 5, No. 3, 417-430 (2007). MSC: 81P68 68R10 PDFBibTeX XMLCite \textit{N. Saxena} et al., Int. J. Quantum Inf. 5, No. 3, 417--430 (2007; Zbl 1119.81042) Full Text: DOI arXiv
Shparlinski, Igor E. Character sums over shifted smooth numbers. (English) Zbl 1166.11028 Proc. Am. Math. Soc. 135, No. 9, 2699-2705 (2007). Reviewer: Chunlei Liu (Shanghai) MSC: 11L40 11N25 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 135, No. 9, 2699--2705 (2007; Zbl 1166.11028) Full Text: DOI
Shparlinski, Igor E. On the distribution of angles of the Salié sums. (English) Zbl 1117.11044 Bull. Aust. Math. Soc. 75, No. 2, 221-227 (2007). Reviewer: Stamatis Koumandos (Nicosia) MSC: 11L05 11L40 11T24 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Bull. Aust. Math. Soc. 75, No. 2, 221--227 (2007; Zbl 1117.11044) Full Text: DOI
Shparlinski, Igor E. On the set of distances between two sets over finite fields. (English) Zbl 1134.11044 Int. J. Math. Math. Sci. 2006, No. 14, Article ID 59482, 5 p. (2006). Reviewer: Jebrel M. Habeb (Irbid) MSC: 11T23 05C12 11L07 12E20 52C10 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Int. J. Math. Math. Sci. 2006, No. 14, Article ID 59482, 5 p. (2006; Zbl 1134.11044) Full Text: DOI EuDML
El-Mahassni, Edwin D.; Shparlinski, Igor E.; Winterhof, Arne Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers. (English) Zbl 1105.11023 Monatsh. Math. 148, No. 4, 297-307 (2006). Reviewer: Zhu Yaochen (Beijing) MSC: 11K45 11L07 65C10 PDFBibTeX XMLCite \textit{E. D. El-Mahassni} et al., Monatsh. Math. 148, No. 4, 297--307 (2006; Zbl 1105.11023) Full Text: DOI
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E. Character sums with exponential functions over smooth numbers. (English) Zbl 1184.11025 Indag. Math., New Ser. 17, No. 2, 157-168 (2006). MSC: 11L07 11L20 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Indag. Math., New Ser. 17, No. 2, 157--168 (2006; Zbl 1184.11025) Full Text: DOI
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. Distribution of harmonic sums and Bernoulli polynomials modulo a prime. (English) Zbl 1158.11035 Math. Z. 253, No. 4, 855-865 (2006). MSC: 11L07 11A07 11B68 PDFBibTeX XMLCite \textit{M. Z. Garaev} et al., Math. Z. 253, No. 4, 855--865 (2006; Zbl 1158.11035) Full Text: DOI
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. Catalan and Apéry numbers in residue classes. (English) Zbl 1101.11010 J. Comb. Theory, Ser. A 113, No. 5, 851-865 (2006). Reviewer: Tom M. Apostol (Pasadena) MSC: 11B65 11A07 11B75 05A10 PDFBibTeX XMLCite \textit{M. Z. Garaev} et al., J. Comb. Theory, Ser. A 113, No. 5, 851--865 (2006; Zbl 1101.11010) Full Text: DOI
Blackburn, Simon R.; Shparlinski, Igor E. Character sums and nonlinear recurrence sequences. (English) Zbl 1108.11060 Discrete Math. 306, No. 12, 1126-1131 (2006). Reviewer: Arne Winterhof (Linz) MSC: 11L07 11B37 11L40 PDFBibTeX XMLCite \textit{S. R. Blackburn} and \textit{I. E. Shparlinski}, Discrete Math. 306, No. 12, 1126--1131 (2006; Zbl 1108.11060) Full Text: DOI
Banks, William D.; Shparlinski, Igor E. Non-residues and primitive roots in Beatty sequences. (English) Zbl 1144.11064 Bull. Aust. Math. Soc. 73, No. 3, 433-443 (2006). Reviewer: Florian Luca (Morelia) MSC: 11L40 11B83 11J71 PDFBibTeX XMLCite \textit{W. D. Banks} and \textit{I. E. Shparlinski}, Bull. Aust. Math. Soc. 73, No. 3, 433--443 (2006; Zbl 1144.11064) Full Text: DOI
Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E. Exponential sums with Dickson polynomials. (English) Zbl 1104.11055 Finite Fields Appl. 12, No. 1, 16-25 (2006). Reviewer: Arne Winterhof (Linz) MSC: 11T23 11T06 11L40 PDFBibTeX XMLCite \textit{D. Gomez-Perez} et al., Finite Fields Appl. 12, No. 1, 16--25 (2006; Zbl 1104.11055) Full Text: DOI
Shparlinski, Igor; Winterhof, Arne Noisy interpolation of sparse polynomials in finite fields. (English) Zbl 1131.11077 Appl. Algebra Eng. Commun. Comput. 16, No. 5, 307-317 (2005). Reviewer: Robert Fitzgerald (Carbondale) MSC: 11T06 11T71 PDFBibTeX XMLCite \textit{I. Shparlinski} and \textit{A. Winterhof}, Appl. Algebra Eng. Commun. Comput. 16, No. 5, 307--317 (2005; Zbl 1131.11077) Full Text: DOI
Banks, William D.; Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. Uniform distribution of the fractional part of the average prime divisor. (English) Zbl 1088.11062 Forum Math. 17, No. 6, 885-901 (2005). Reviewer: Mongi Naimi (Tunis) MSC: 11K65 11L07 11N37 11N60 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Forum Math. 17, No. 6, 885--901 (2005; Zbl 1088.11062) Full Text: DOI
Hess, Florian; Shparlinski, Igor E. On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. (English) Zbl 1116.14307 Des. Codes Cryptography 35, No. 1, 111-117 (2005). MSC: 65C10 11T23 14H52 PDFBibTeX XMLCite \textit{F. Hess} and \textit{I. E. Shparlinski}, Des. Codes Cryptography 35, No. 1, 111--117 (2005; Zbl 1116.14307) Full Text: DOI
Shparlinski, Igor; Winterhof, Arne A hidden number problem in small subgroups. (English) Zbl 1072.11092 Math. Comput. 74, No. 252, 2073-2080 (2005). MSC: 11T23 11T71 11Y16 94A60 PDFBibTeX XMLCite \textit{I. Shparlinski} and \textit{A. Winterhof}, Math. Comput. 74, No. 252, 2073--2080 (2005; Zbl 1072.11092) Full Text: DOI
Banks, William D.; Luca, Florian; Shparlinski, Igor E. Irrationality of power series for various number theoretic functions. (English) Zbl 1072.11002 Manuscr. Math. 117, No. 2, 183-197 (2005). Reviewer: Ali Benhissi (Monastir) MSC: 11A25 11J72 11K65 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Manuscr. Math. 117, No. 2, 183--197 (2005; Zbl 1072.11002) Full Text: DOI Link
Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. (English) Zbl 1068.11043 J. Number Theory 112, No. 2, 216-237 (2005). Reviewer: Peter Shiu (Loughborough) MSC: 11G20 11T99 11L07 11N69 PDFBibTeX XMLCite \textit{A. Granville} et al., J. Number Theory 112, No. 2, 216--237 (2005; Zbl 1068.11043) Full Text: DOI
Cohen, Stephen D.; Dewar, Michael; Friedlander, John B.; Panario, Daniel; Shparlinski, Igor E. Polynomial Gauss sums. (English) Zbl 1084.11048 Proc. Am. Math. Soc. 133, No. 8, 2225-2231 (2005). Reviewer: Angel V. Kumchev (Towson) MSC: 11L07 11B50 11K31 11L05 11T23 PDFBibTeX XMLCite \textit{S. D. Cohen} et al., Proc. Am. Math. Soc. 133, No. 8, 2225--2231 (2005; Zbl 1084.11048) Full Text: DOI
Blackburn, Simon R.; Gomez-Perez, Domingo; Gutierrez, Jaime; Shparlinski, Igor E. Predicting nonlinear pseudorandom number generators. (English) Zbl 1136.11316 Math. Comput. 74, No. 251, 1471-1494 (2005). MSC: 11K45 94A60 PDFBibTeX XMLCite \textit{S. R. Blackburn} et al., Math. Comput. 74, No. 251, 1471--1494 (2005; Zbl 1136.11316) Full Text: DOI
Shparlinski, Igor E. On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA. (English) Zbl 1173.68508 Inf. Process. Lett. 92, No. 3, 143-147 (2004). MSC: 94A60 11T71 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Inf. Process. Lett. 92, No. 3, 143--147 (2004; Zbl 1173.68508) Full Text: DOI
Dewar, Michael; Panario, Daniel; Shparlinski, Igor E. Distribution of exponential functions with \(k\)-full exponent modulo a prime. (English) Zbl 1161.11369 Indag. Math., New Ser. 15, No. 4, 497-503 (2004). MSC: 11L05 PDFBibTeX XMLCite \textit{M. Dewar} et al., Indag. Math., New Ser. 15, No. 4, 497--503 (2004; Zbl 1161.11369) Full Text: DOI
Shparlinski, Igor E. Distribution of exponential functions with squarefull exponent in residue rings. (English) Zbl 1108.11070 Indag. Math., New Ser. 15, No. 2, 283-289 (2004). Reviewer: Mongi Naimi (Tunis) MSC: 11N37 11N25 11T23 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Indag. Math., New Ser. 15, No. 2, 283--289 (2004; Zbl 1108.11070) Full Text: DOI
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. Character sums and congruences with \(n!\). (English) Zbl 1060.11046 Trans. Am. Math. Soc. 356, No. 12, 5089-5102 (2004). Reviewer: George Greaves (Cardiff) MSC: 11L40 11B65 11A07 PDFBibTeX XMLCite \textit{M. Z. Garaev} et al., Trans. Am. Math. Soc. 356, No. 12, 5089--5102 (2004; Zbl 1060.11046) Full Text: DOI arXiv
Shparlinski, Igor E. Bounds of Gauss sums in finite fields. (English) Zbl 1195.11108 Proc. Am. Math. Soc. 132, No. 10, 2817-2824 (2004). MSC: 11L05 11T24 11B37 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 132, No. 10, 2817--2824 (2004; Zbl 1195.11108) Full Text: DOI
Conflitti, Alessandro; Shparlinski, Igor E. On the multidimensional distribution of the subset sum generator of pseudorandom numbers. (English) Zbl 1045.11055 Math. Comput. 73, No. 246, 1005-1011 (2004). Reviewer: Zhu Yaochen (Beijing) MSC: 11K45 11T71 11T23 94A60 PDFBibTeX XMLCite \textit{A. Conflitti} and \textit{I. E. Shparlinski}, Math. Comput. 73, No. 246, 1005--1011 (2004; Zbl 1045.11055) Full Text: DOI
Niederreiter, Harald; Shparlinski, Igor E. On the average distribution of inversive pseudorandom numbers. (English) Zbl 1027.11054 Finite Fields Appl. 8, No. 4, 491-503 (2002). Reviewer: Arne Winterhof (Linz) MSC: 11K45 11K38 65C10 11L07 11T23 PDFBibTeX XMLCite \textit{H. Niederreiter} and \textit{I. E. Shparlinski}, Finite Fields Appl. 8, No. 4, 491--503 (2002; Zbl 1027.11054) Full Text: DOI
Shparlinski, Igor E. On the distribution of the Diffie-Hellman pairs. (English) Zbl 1003.11059 Finite Fields Appl. 8, No. 2, 131-141 (2002). Reviewer: Pei Dingyi (Beijing) MSC: 11T71 11K45 94A60 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Finite Fields Appl. 8, No. 2, 131--141 (2002; Zbl 1003.11059) Full Text: DOI
González Vasco, Maria Isabel; Shparlinski, Igor E. Security of the most significant bits of the Shamir message passing scheme. (English) Zbl 1021.11032 Math. Comput. 71, No. 237, 333-342 (2002). Reviewer: Enric Nart Viñals (Bellaterra) MSC: 11T71 94A60 11T23 94A62 PDFBibTeX XMLCite \textit{M. I. González Vasco} and \textit{I. E. Shparlinski}, Math. Comput. 71, No. 237, 333--342 (2002; Zbl 1021.11032) Full Text: DOI
Cohen, S. D.; Niederreiter, H.; Shparlinski, I. E.; Zieve, M. Incomplete character sums and a special class of permutations. (English) Zbl 1065.11097 J. Théor. Nombres Bordx. 13, No. 1, 53-63 (2001). Reviewer: Tanja Lange (Lyngby) MSC: 11T24 11L40 11K45 11T71 PDFBibTeX XMLCite \textit{S. D. Cohen} et al., J. Théor. Nombres Bordx. 13, No. 1, 53--63 (2001; Zbl 1065.11097) Full Text: DOI Numdam EuDML EMIS
Shparlinski, Igor E. On the uniformity of distribution of the Naor-Reingold pseudo-random function. (English) Zbl 0998.11041 Finite Fields Appl. 7, No. 2, 318-326 (2001). Reviewer: Arne Winterhof (Wien) MSC: 11K45 11K31 94A60 11T71 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Finite Fields Appl. 7, No. 2, 318--326 (2001; Zbl 0998.11041) Full Text: DOI
Friedlander, John B.; Shparlinski, Igor E. On the distribution of the power generator. (English) Zbl 1029.11042 Math. Comput. 70, No. 236, 1575-1589 (2001). Reviewer: T.Helleseth (Bergen) MSC: 11K45 11L07 94A60 11T23 11T71 PDFBibTeX XMLCite \textit{J. B. Friedlander} and \textit{I. E. Shparlinski}, Math. Comput. 70, No. 236, 1575--1589 (2001; Zbl 1029.11042) Full Text: DOI
Niederreiter, Harald; Shparlinski, Igor E. On the distribution of inversive congruential pseudorandom numbers in parts of the period. (English) Zbl 0983.11048 Math. Comput. 70, No. 236, 1569-1574 (2001). Reviewer: Robert F. Tichy (Graz) MSC: 11K45 65C10 11L07 11T23 11K38 PDFBibTeX XMLCite \textit{H. Niederreiter} and \textit{I. E. Shparlinski}, Math. Comput. 70, No. 236, 1569--1574 (2001; Zbl 0983.11048) Full Text: DOI
Friedlander, John B.; Shparlinski, Igor E. Double exponential sums over thin sets. (English) Zbl 1013.11046 Proc. Am. Math. Soc. 129, No. 6, 1617-1621 (2001). Reviewer: Jürgen Hinz (Marburg) MSC: 11L07 11T23 11L26 PDFBibTeX XMLCite \textit{J. B. Friedlander} and \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 129, No. 6, 1617--1621 (2001; Zbl 1013.11046) Full Text: DOI
Shparlinski, Igor E. Linear complexity of the Naor-Reingold pseudo-random function. (English) Zbl 1339.94065 Inf. Process. Lett. 76, No. 3, 95-99 (2000). MSC: 94A60 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Inf. Process. Lett. 76, No. 3, 95--99 (2000; Zbl 1339.94065) Full Text: DOI Link
Friedlander, John B.; Hansen, Jan; Shparlinski, Igor E. Character sums with exponential functions. (English) Zbl 1017.11045 Mathematika 47, No. 1-2, 75-85 (2000). Reviewer: Arne Winterhof (Wien) MSC: 11L07 11T23 11T24 PDFBibTeX XMLCite \textit{J. B. Friedlander} et al., Mathematika 47, No. 1--2, 75--85 (2000; Zbl 1017.11045) Full Text: DOI
Canetti, Ran; Friedlander, John; Konyagin, Sergei; Larsen, Michael; Lieman, Daniel; Shparlinski, Igor On the statistical properties of Diffie-Hellman distributions. (English) Zbl 0997.11066 Isr. J. Math. 120, Pt. A, 23-46 (2000). Reviewer: Arne Winterhof (Wien) MSC: 11L07 11T23 94A60 11T71 PDFBibTeX XMLCite \textit{R. Canetti} et al., Isr. J. Math. 120, Part A, 23--46 (2000; Zbl 0997.11066) Full Text: DOI
von zur Gathen, Joachim; Karpinski, Marek; Shparlinski, Igor Counting curves and their projections. (English) Zbl 0990.68642 Comput. Complexity 6(1996-97), No. 1, 64-99 (1997). Reviewer: Joos Heintz (MR 98d:68111) MSC: 68W30 14Q05 68Q15 68Q25 68Q17 PDFBibTeX XMLCite \textit{J. von zur Gathen} et al., Comput. Complexity 6, No. 1, 64--99 (1997; Zbl 0990.68642) Full Text: DOI
Shparlinski, Igor E. Finding irreducible and primitive polynomials. (English) Zbl 0797.11094 Appl. Algebra Eng. Commun. Comput. 4, No. 4, 263-268 (1993). Reviewer: G.Steidl (Darmstadt) MSC: 11T06 11Y16 12E05 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Appl. Algebra Eng. Commun. Comput. 4, No. 4, 263--268 (1993; Zbl 0797.11094) Full Text: DOI
Shparlinski, Igor E. On bivariate polynomial factorization over finite fields. (English) Zbl 0777.11055 Math. Comput. 60, No. 202, 787-791 (1993). Reviewer: I.F.Blake (Waterloo / Ontario) MSC: 11T06 12E05 11Y40 12Y05 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Math. Comput. 60, No. 202, 787--791 (1993; Zbl 0777.11055) Full Text: DOI