Edit Profile (opens in new tab) Granville, Andrew James Co-Author Distance Author ID: granville.andrew-j Published as: Granville, Andrew; Granville, A.; Granville, Andrew J. more...less Homepage: https://dms.umontreal.ca/~andrew/ External Links: MGP · Wikidata · Google Scholar · MathOverflow · dblp · GND · IdRef · theses.fr Videos: carmin.tv Documents Indexed: 186 Publications since 1985, including 3 Books and 6 Additional arXiv Preprints 6 Contributions as Editor · 2 Further Contributions Reviewing Activity: 56 Reviews Co-Authors: 126 Co-Authors with 124 Joint Publications 4,347 Co-Co-Authors all top 5 Co-Authors 68 single-authored 21 Soundararajan, Kannan 7 Pomerance, Carl Bernard 6 Friedlander, John Benjamin 5 Koukoulopoulos, Dimitris 4 Moisiadis, Alexandros 3 Harper, Adam J. 3 Rees, Rolf Stephen 3 Rudnick, Zeév 3 Shao, Xuancheng 3 Solymosi, József 3 Walker, Aled 2 Alford, William Robert 2 Balog, Antal 2 Cilleruelo, Javier 2 Croot, Ernie 2 de la Bretèche, Régis 2 Erdős, Pál 2 Fraser, Maia 2 Harris, Michael Howard 2 Martin, Greg 2 McLarty, Colin 2 Mollin, Richard Anthony 2 Pemantle, Robin 2 Riehl, Emily 2 Shakan, George 2 Shallit, Jeffrey Outlaw 2 Tetali, Prasad 2 Tucker, Thomas John 2 Venkatesh, Akshay 2 Wigman, Igor 2 Williams, Hugh Cowie 1 Adhikari, Sukumar Das 1 Agoh, Takashi 1 Alladi, Krishnaswami 1 Almkvist, Gert 1 Alon, Noga 1 Biró, András 1 Blomer, Valentin 1 Bober, Jonathan W. 1 Bombieri, Enrico 1 Brock, Bradley W. 1 Brüdern, Jörg 1 Cai, Tianxin 1 Calkin, Neil J. 1 Canfield, Rod 1 Cherubini, Giacomo 1 Conrey, John Brian 1 Croot, Ernest S. III 1 Cutter, Pamela A. 1 Darmon, Henri René 1 De Koninck, Jean-Marie 1 Deshouillers, Jean-Marc 1 Donnelly, Stephen 1 Drappeau, Sary 1 Dummit, David S. 1 Elkies, Noam David 1 Elliott, Peter D. T. A. 1 Enflo, Per Henrik 1 Faber, Xander 1 Fazzari, Alessandro 1 Fee, Greg J. 1 Filaseta, Michael A. 1 Fisher, Tom A. 1 Ford, Kevin B. 1 Fung, Gilbert W. 1 Gabdullin, Mikhail R. 1 Goldmakher, Leo 1 Goulden, Ian P. 1 Grantham, Jon 1 Granville, Jennifer 1 Gronau, Hans-Dietrich O. F. 1 Hartman, Alan 1 Havil, Julian 1 Hildebrand, Adolf J. 1 Jiménez-Urroz, Jorge 1 Kala, Vítězslav 1 Kamienny, Sheldon 1 Kane, Daniel M. 1 Kisilevsky, Hershy 1 Kurlberg, Pär 1 Łaba, Izabella 1 Lamzouri, Youness 1 Lemke Oliver, Robert J. 1 Li, Shuguang 1 Luca, Florian 1 Lumley, Allysa 1 Maier, Helmut 1 Mangerel, Alexander P. 1 Matomäki, Kaisa 1 Maynard, James 1 Mazur, Barry 1 Monagan, Michael B. 1 Mullin, Ronald Cleveland 1 Narkiewicz, Władysław 1 Nathanson, Melvyn Bernard 1 Ono, Ken 1 Perelli, Alberto 1 Pintz, Janos 1 Pleasants, Peter A. B. 1 Poonen, Bjorn ...and 29 more Co-Authors all top 5 Serials 9 American Mathematical Monthly 7 Acta Arithmetica 7 Bulletin of the American Mathematical Society. New Series 6 Journal of Number Theory 5 Annals of Mathematics. Second Series 4 Mathematics of Computation 4 Mathematika 4 Notices of the American Mathematical Society 4 The Ramanujan Journal 3 Canadian Journal of Mathematics 3 Duke Mathematical Journal 3 Journal of Combinatorial Theory. Series A 3 Proceedings of the American Mathematical Society 3 Transactions of the American Mathematical Society 3 Journal of the American Mathematical Society 3 IMRN. International Mathematics Research Notices 3 The Quarterly Journal of Mathematics 3 La Gaceta de la Real Sociedad Matemática Española 2 Advances in Mathematics 2 Bulletin of the London Mathematical Society 2 Canadian Mathematical Bulletin 2 Compositio Mathematica 2 Functiones et Approximatio. Commentarii Mathematici 2 Inventiones Mathematicae 2 Journal of the London Mathematical Society. Second Series 2 Comptes Rendus Mathématiques de l’Académie des Sciences 2 Geometric and Functional Analysis. GAFA 2 Philosophical Transactions of the Royal Society of London. Series A 2 Experimental Mathematics 2 The Electronic Journal of Combinatorics 2 Journal of the European Mathematical Society (JEMS) 2 International Journal of Number Theory 2 CRM Proceedings & Lecture Notes 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Lithuanian Mathematical Journal 1 Linear and Multilinear Algebra 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Acta Mathematica 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin de la Société Mathématique de France 1 The Fibonacci Quarterly 1 Gazette des Mathématiciens 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Scandinavian Actuarial Journal 1 Journal of Sichuan University. Natural Science Edition 1 Combinatorica 1 Acta Mathematica Hungarica 1 Graphs and Combinatorics 1 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Aequationes Mathematicae 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Expositiones Mathematicae 1 Journal de Théorie des Nombres de Bordeaux 1 Finite Fields and their Applications 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Acta Mathematica Sinica. English Series 1 Integers 1 Milan Journal of Mathematics 1 Developments in Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Rivista di Matematica della Università di Parma. New Series 1 Forum of Mathematics, Sigma 1 Annales Mathématiques du Québec 1 Research in Number Theory 1 Princeton Science Library all top 5 Fields 172 Number theory (11-XX) 24 Combinatorics (05-XX) 10 General and overarching topics; collections (00-XX) 7 History and biography (01-XX) 7 Computer science (68-XX) 6 Algebraic geometry (14-XX) 5 Field theory and polynomials (12-XX) 3 Group theory and generalizations (20-XX) 3 Probability theory and stochastic processes (60-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 160 Publications have been cited 2,136 times in 1,766 Documents Cited by ▼ Year ▼ Arithmetic properties of binomial coefficients. I: Binomial coefficients modulo prime powers. Zbl 0903.11005 Granville, Andrew 131 1997 Defect zero \(p\)-blocks for finite simple groups. Zbl 0855.20007 Granville, Andrew; Ono, Ken 128 1996 There are infinitely many Carmichael numbers. Zbl 0816.11005 Alford, W. R.; Granville, Andrew; Pomerance, Carl 125 1994 On the equations \(z^ m = F(x,y)\) and \(Ax^ p + By^ q = Cz^ r\). Zbl 0838.11023 Darmon, Henri; Granville, Andrew 95 1995 The distribution of values of \(L(1,\chi_d)\). Zbl 1044.11080 Granville, Andrew; Soundararajan, K. 73 2003 A decomposition of Riemann’s zeta-function. Zbl 0907.11024 Granville, Andrew 70 1997 Smooth numbers: computational number theory and beyond. Zbl 1230.11157 Granville, Andrew 67 2008 \(abc\) allows us to count squarefrees. Zbl 0924.11018 Granville, Andrew 67 1998 Large character sums: pretentious characters and the Pólya-Vinogradov theorem. Zbl 1210.11090 Granville, Andrew; Soundararajan, K. 66 2007 Harald Cramér and the distribution of prime numbers. Zbl 0833.01018 Granville, Andrew 47 1995 Large character sums. Zbl 0983.11053 Granville, Andrew; Soundararajan, K. 47 2001 Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Zbl 0868.11009 Granville, Andrew; Ramaré, Olivier 33 1996 Prime number races. Zbl 1139.11037 Granville, Andrew; Martin, Greg 33 2006 The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042 Granville, Andrew; Wigman, Igor 31 2011 It’s as easy as \(abc\). Zbl 1160.11318 Granville, Andrew; Tucker, Thomas J. 29 2002 Extreme values of \(|\zeta(1+it)|\). Zbl 1131.11055 Granville, Andrew; Soundararajan, K. 28 2006 Limitations to the equi-distribution of primes. I. Zbl 0671.10041 Friedlander, John; Granville, Andrew 27 1989 Sieving and the Erdős-Kac theorem. Zbl 1145.11071 Granville, Andrew; Soundararajan, K. 27 2007 On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034 Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C. 26 1990 Decay of mean values of multiplicative functions. Zbl 1047.11093 Granville, Andrew; Soundararajan, K. 25 2003 Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012 Kamienny, S.; Mazur, B. 22 1995 \(ABC\) implies no “Siegel zeros” for \(L\)-functions of characters with negative discriminant. Zbl 0967.11033 Granville, Andrew; Stark, H. M. 21 2000 Primes in intervals of bounded length. Zbl 1319.11064 Granville, Andrew 20 2015 Prime factors of dynamical sequences. Zbl 1290.11019 Faber, Xander; Granville, Andrew 19 2011 Unexpected irregularities in the distribution of prime numbers. Zbl 0843.11043 Granville, Andrew 19 1995 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058 Cilleruelo, Javier; Granville, Andrew 19 2007 The spectrum of multiplicative functions. Zbl 1036.11042 Granville, Andrew; Soundararajan, K. 18 2001 A new proof of Halász’s theorem, and its consequences. Zbl 1443.11200 Granville, Andrew; Harper, Adam J.; Soundararajan, K. 17 2019 On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. Zbl 1068.11043 Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru 16 2005 Squares in arithmetic progressions. Zbl 0771.11034 Bombieri, Enrico; Granville, Andrew; Pintz, János 16 1992 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067 Granville, Andrew; Pomerance, Carl 15 2002 Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012 Granville, Andrew; Wigman, Igor 15 2017 Estimates for representation numbers of quadratic forms. Zbl 1135.11020 Blomer, Valentin; Granville, Andrew 15 2006 Borwein and Bradley’s Apéry-like formulae for \(\zeta(4n+3)\). Zbl 0976.11035 Almkvist, Gert; Granville, Andrew 15 1999 Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032 Granville, Andrew; Soundararajan, Kannan 14 2008 Multiplicative functions in arithmetic progressions. Zbl 1306.11078 Balog, Antal; Granville, Andrew; Soundararajan, Kannan 14 2013 Some conjectures related to Fermat’s Last Theorem. Zbl 0702.11015 Granville, Andrew 14 1990 Upper bounds for \(|L(1,\chi)|\). Zbl 1022.11041 Granville, Andrew; Soundararajan, K. 14 2002 Integers, without large prime factors, in arithmetic progressions. I. Zbl 0784.11045 Granville, Andrew 13 1993 On the difficulty of finding reliable witnesses. Zbl 0828.11074 Alford, W. R.; Granville, Andrew; Pomerance, Carl 13 1994 Oscillation theorems for primes in arithmetic progressions and for sifting functions. Zbl 0724.11040 Friedlander, John; Granville, Andrew; Hildebrand, Adolf; Maier, Helmut 13 1991 Subdesigns in Steiner quadruple systems. Zbl 0726.05017 Granville, Andrew; Hartman, Alan 13 1991 Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028 Granville, Andrew 13 2007 The square of the Fermat quotient. Zbl 1083.11005 Granville, Andrew 13 2004 More points than expected on curves over finite field extensions. Zbl 1023.11029 Brock, Bradley W.; Granville, Andrew 13 2001 Values of Bernoulli polynomials. Zbl 0856.11008 Granville, Andrew; Sun, Zhi-Wei 12 1996 The first case of Fermat’s last theorem is true for all prime exponents up to \(714,591,416,091,389\). Zbl 0645.10018 Granville, Andrew; Monagan, Michael B. 11 1988 Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123 Granville, Andrew 11 2007 When the sieve works. Zbl 1326.11055 Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa 11 2015 The frequency and the structure of large character sums. Zbl 1409.11079 Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris 11 2018 On the size of the first factor of the class number of a cyclotomic field. Zbl 0701.11051 Granville, A. 11 1990 Prime divisors are Poisson distributed. Zbl 1118.11005 Granville, Andrew 11 2007 Big biases amongst products of two primes. Zbl 1347.11067 Dummit, David; Granville, Andrew; Kisilevsky, Hershy 10 2016 Zaphod Beeblebrox’s brain and the fifty-ninth row of Pascal’s triangle. Zbl 0757.05003 Granville, Andrew 10 1992 An uncertainty principle for arithmetic sequences. Zbl 1139.11040 Granville, Andrew; Soundararajan, K. 10 2007 Prime suspects. The anatomy of integers and permutations. Illustrated by Robert J. Lewis. Zbl 1423.00004 Granville, Andrew; Granville, Jennifer 10 2019 On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005 Cai, Tianxin; Granville, Andrew 10 2002 Bombieri-Vinogradov for multiplicative functions, and beyond the \(x^{1/2}\)-barrier. Zbl 1473.11185 Granville, Andrew; Shao, Xuancheng 10 2019 On the exponential sum over \(k\)-free numbers. Zbl 0922.11071 Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D. 10 1998 The Frobenius postage stamp problem, and beyond. Zbl 07301143 Granville, A.; Shakan, G. 10 2020 Integers, without large prime factors, in arithmetic progressions. II. Zbl 0792.11036 Granville, Andrew 9 1993 Large character sums: Burgess’s theorem and zeros of \(L\)-functions. Zbl 1444.11177 Granville, Andrew; Soundararajan, Kannan 9 2018 Nested Steiner n-cycle systems and perpendicular arrays. Zbl 0732.05006 Granville, A.; Moisiadis, A.; Rees, R. 9 1988 Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001 Granville, Andrew 9 2006 Beyond the LSD method for the partial sums of multiplicative functions. Zbl 1455.11128 Granville, Andrew; Koukoulopoulos, Dimitris 9 2019 Checking the Goldbach conjecture on a vector computer. Zbl 0679.10002 Granville, A.; Van de Lune, J.; te Riele, H. J. J. 8 1989 Mean values of multiplicative functions over function fields. Zbl 1394.11069 Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 8 2015 Ranks of quadratic twists of elliptic curves. Zbl 1365.11070 Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F. 8 2014 It is easy to determine whether a given integer is prime. Zbl 1110.11002 Granville, Andrew 8 2005 On sharp transitions in making squares. Zbl 1321.11122 Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad 8 2012 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039 Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 7 1992 Visibility in the plane. Zbl 1176.11027 Adhikari, Sukumar Das; Granville, Andrew 7 2009 On complementary decompositions of the complete graph. Zbl 0674.05050 Granville, Andrew; Moisiadis, Alexandros; Rees, Rolf 7 1989 On pairs of coprime integers with no large prime factors. Zbl 0745.11043 Granville, Andrew 7 1991 Corrigendum to “Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis”. Zbl 1235.11092 Granville, Andrew 7 2008 Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109 Granville, Andrew; Kurlberg, Pär 7 2008 Smooth-supported multiplicative functions in arithmetic progressions beyond the \(x^{1/2}\)-barrier. Zbl 1428.11174 Drappeau, Sary; Granville, Andrew; Shao, Xuancheng 7 2017 A tight structure theorem for sumsets. Zbl 1496.11048 Granville, Andrew; Walker, Aled 7 2021 Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129 Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej 7 2008 Different approaches to the distribution of primes. Zbl 1275.11129 Granville, Andrew 6 2010 On the least prime in certain arithmetic progression. Zbl 0658.10049 Granville, Andrew; Pomerance, Carl 6 1990 The prime factors of Wendt’s binomial circulant determinant. Zbl 0767.11059 Fee, Greg; Granville, Andrew 6 1991 Limitations to the equi-distribution of primes. IV. Zbl 0736.11049 Friedlander, John; Granville, Andrew 6 1991 Powerful numbers and Fermat’s Last Theorem. Zbl 0595.10011 Granville, Andrew 6 1986 Smoothing ‘smooth’ numbers. Zbl 0795.11041 Friedlander, John B.; Granville, Andrew 6 1993 The number of sumsets in a finite field. Zbl 1223.11028 Alon, Noga; Granville, Andrew; Ubis, Adrián 6 2010 On positive integers \(\leq x\) with prime factors \(\leq t\,\log \,x\). Zbl 0686.10031 Granville, Andrew 6 1989 A note on sums of primes. Zbl 0691.10039 Granville, Andrew 6 1990 Aurifeuillian factorization. Zbl 1107.11050 Granville, Andrew; Pleasants, Peter 6 2006 A more intuitive proof of a sharp version of Halász’s theorem. Zbl 1456.11182 Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 6 2018 When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105 Granville, Andrew; Shao, Xuancheng 6 2018 The number of fields generated by the square root of values of a given polynomial. Zbl 1044.11087 Cutter, Pamela; Granville, Andrew; Tucker, Thomas J. 6 2003 A binary additive problem of Erdős and the order of \(2 \bmod {p^2}\). Zbl 0912.11003 Granville, Andrew; Soundararajan, K. 6 1998 On a paper of Agur, Fraenkel and Klein. Zbl 0755.05005 Granville, Andrew 5 1991 Relevance of the residue class to the abundance of primes. Zbl 0795.11040 Friedlander, John B.; Granville, Andrew 5 1992 Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011 Balog, Antal; Granville, Andrew; Solymosi, Jozsef 5 2017 Sum-product formulae. Zbl 1407.11043 Granville, Andrew; Solymosi, József 5 2016 Squares in arithmetic progressions and infinitely many primes. Zbl 1391.11115 Granville, Andrew 5 2017 Representing binomial coefficients as sums of squares. Zbl 0717.11016 Granville, Andrew; Zhu, Yiliang 5 1990 Consecutive real quadratic fields with large class numbers. Zbl 1532.11152 Cherubini, Giacomo; Fazzari, Alessandro; Granville, Andrew; Kala, Vítězslav; Yatsyna, Pavlo 4 2023 Three conjectures about character sums. Zbl 1533.11150 Granville, Andrew; Mangerel, Alexander P. 3 2023 Primes in short intervals: heuristics and calculations. Zbl 07708950 Granville, Andrew; Lumley, Allysa 3 2023 Effective results on the size and structure of sumsets. Zbl 07794394 Granville, Andrew; Shakan, George; Walker, Aled 2 2023 Exponential sums with multiplicative coefficients and applications. Zbl 1505.11124 de la Bretèche, Régis; Granville, Andrew 2 2022 The man who loved problems: Richard K. Guy. Zbl 1493.01053 Granville, Andrew; Pomerance, Carl 1 2022 Sieving intervals and Siegel zeros. Zbl 1504.11089 Granville, Andrew 1 2022 A tight structure theorem for sumsets. Zbl 1496.11048 Granville, Andrew; Walker, Aled 7 2021 An alternative to Vaughan’s identity. Zbl 1482.11123 Granville, Andrew 1 2021 The Frobenius postage stamp problem, and beyond. Zbl 07301143 Granville, A.; Shakan, G. 10 2020 A new proof of Halász’s theorem, and its consequences. Zbl 1443.11200 Granville, Andrew; Harper, Adam J.; Soundararajan, K. 17 2019 Prime suspects. The anatomy of integers and permutations. Illustrated by Robert J. Lewis. Zbl 1423.00004 Granville, Andrew; Granville, Jennifer 10 2019 Bombieri-Vinogradov for multiplicative functions, and beyond the \(x^{1/2}\)-barrier. Zbl 1473.11185 Granville, Andrew; Shao, Xuancheng 10 2019 Beyond the LSD method for the partial sums of multiplicative functions. Zbl 1455.11128 Granville, Andrew; Koukoulopoulos, Dimitris 9 2019 Natural exact covering systems and the reversion of the Möbius series. Zbl 1427.05022 Goulden, I. P.; Granville, Andrew; Richmond, L. Bruce; Shallit, Jeffrey 4 2019 Number theory revealed: a masterclass. Zbl 1454.11002 Granville, Andrew 4 2019 Number theory revealed: an introduction. Zbl 1454.11001 Granville, Andrew 1 2019 The frequency and the structure of large character sums. Zbl 1409.11079 Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris 11 2018 Large character sums: Burgess’s theorem and zeros of \(L\)-functions. Zbl 1444.11177 Granville, Andrew; Soundararajan, Kannan 9 2018 A more intuitive proof of a sharp version of Halász’s theorem. Zbl 1456.11182 Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 6 2018 When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105 Granville, Andrew; Shao, Xuancheng 6 2018 Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012 Granville, Andrew; Wigman, Igor 15 2017 Smooth-supported multiplicative functions in arithmetic progressions beyond the \(x^{1/2}\)-barrier. Zbl 1428.11174 Drappeau, Sary; Granville, Andrew; Shao, Xuancheng 7 2017 Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011 Balog, Antal; Granville, Andrew; Solymosi, Jozsef 5 2017 Squares in arithmetic progressions and infinitely many primes. Zbl 1391.11115 Granville, Andrew 5 2017 Big biases amongst products of two primes. Zbl 1347.11067 Dummit, David; Granville, Andrew; Kisilevsky, Hershy 10 2016 Sum-product formulae. Zbl 1407.11043 Granville, Andrew; Solymosi, József 5 2016 Primes in intervals of bounded length. Zbl 1319.11064 Granville, Andrew 20 2015 When the sieve works. Zbl 1326.11055 Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa 11 2015 Mean values of multiplicative functions over function fields. Zbl 1394.11069 Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 8 2015 Best possible densities of Dickson \(m\)-tuples, as a consequence of Zhang-Maynard-Tao. Zbl 1391.11116 Granville, Andrew; Kane, Daniel M.; Koukoulopoulos, Dimitris; Oliver, Robert J. Lemke 4 2015 About the cover: a new mathematical celebrity. Zbl 1310.01017 Granville, Andrew 1 2015 What is the best approach to counting primes? Zbl 1541.11003 Granville, Andrew 1 2015 Ranks of quadratic twists of elliptic curves. Zbl 1365.11070 Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F. 8 2014 Friable density. (Densité des friables.) Zbl 1318.11121 de la Bretèche, Régis; Granville, Andrew 3 2014 Multiplicative functions in arithmetic progressions. Zbl 1306.11078 Balog, Antal; Granville, Andrew; Soundararajan, Kannan 14 2013 On sharp transitions in making squares. Zbl 1321.11122 Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad 8 2012 Zeta functions for ideal classes in real quadratic fields, at \(s=0\). Zbl 1276.11180 Biró, András; Granville, Andrew 5 2012 Primitive prime factors in second-order linear recurrence sequences. Zbl 1272.11027 Granville, Andrew 1 2012 The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042 Granville, Andrew; Wigman, Igor 31 2011 Prime factors of dynamical sequences. Zbl 1290.11019 Faber, Xander; Granville, Andrew 19 2011 Different approaches to the distribution of primes. Zbl 1275.11129 Granville, Andrew 6 2010 The number of sumsets in a finite field. Zbl 1223.11028 Alon, Noga; Granville, Andrew; Ubis, Adrián 6 2010 Visibility in the plane. Zbl 1176.11027 Adhikari, Sukumar Das; Granville, Andrew 7 2009 Close lattice points on circles. Zbl 1229.11124 Cilleruelo, Javier; Granville, Andrew 4 2009 Pretentiousness in analytic number theory. Zbl 1236.11086 Granville, Andrew 3 2009 Smooth numbers: computational number theory and beyond. Zbl 1230.11157 Granville, Andrew 67 2008 Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032 Granville, Andrew; Soundararajan, Kannan 14 2008 Corrigendum to “Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis”. Zbl 1235.11092 Granville, Andrew 7 2008 Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109 Granville, Andrew; Kurlberg, Pär 7 2008 Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129 Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej 7 2008 Prime number patterns. Zbl 1145.11069 Granville, Andrew 2 2008 Running time predictions for factoring algorithms. Zbl 1205.11132 Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad 1 2008 Anatomy of integers. Based on the CRM workshop, Montreal, Canada, March 13–17, 2006. Zbl 1142.11002 1 2008 Large character sums: pretentious characters and the Pólya-Vinogradov theorem. Zbl 1210.11090 Granville, Andrew; Soundararajan, K. 66 2007 Sieving and the Erdős-Kac theorem. Zbl 1145.11071 Granville, Andrew; Soundararajan, K. 27 2007 Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058 Cilleruelo, Javier; Granville, Andrew 19 2007 Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028 Granville, Andrew 13 2007 Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123 Granville, Andrew 11 2007 Prime divisors are Poisson distributed. Zbl 1118.11005 Granville, Andrew 11 2007 An uncertainty principle for arithmetic sequences. Zbl 1139.11040 Granville, Andrew; Soundararajan, K. 10 2007 The distribution of roots of a polynomial. Zbl 1170.11016 Granville, Andrew 5 2007 Equidistribution in number theory, an introduction. Proceedings of the NATO Advanced Study Institute on equidistribution in number theory, Montréal, Canada, July 11–22, 2005. Zbl 1121.11004 5 2007 Negative values of truncations to \(L(1,\chi)\). Zbl 1214.11093 Granville, Andrew; Soundararajan, K. 4 2007 Uniform distribution. Zbl 1142.11054 Granville, Andrew; Rudnick, Zeév 4 2007 Torsion points on curves. Zbl 1172.11020 Granville, Andrew; Rudnick, Zeév 4 2007 Erratum: Prime divisors are Poisson distributed. Zbl 1234.11126 Granville, Andrew 3 2007 An introduction to additive combinatorics. Zbl 1183.11007 Granville, Andrew 3 2007 Prime number races. Zbl 1139.11037 Granville, Andrew; Martin, Greg 33 2006 Extreme values of \(|\zeta(1+it)|\). Zbl 1131.11055 Granville, Andrew; Soundararajan, K. 28 2006 Estimates for representation numbers of quadratic forms. Zbl 1135.11020 Blomer, Valentin; Granville, Andrew 15 2006 Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001 Granville, Andrew 9 2006 Aurifeuillian factorization. Zbl 1107.11050 Granville, Andrew; Pleasants, Peter 6 2006 Residue races. Zbl 1161.11300 Granville, Andrew; Shiu, Daniel; Shiu, Peter 2 2006 On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. Zbl 1068.11043 Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru 16 2005 It is easy to determine whether a given integer is prime. Zbl 1110.11002 Granville, Andrew 8 2005 Prime number races. Zbl 1358.11139 Granville, Andrew; Martin, Greg 1 2005 The square of the Fermat quotient. Zbl 1083.11005 Granville, Andrew 13 2004 Errata to: The distribution of values of \(L(1,\chi_d)\). Zbl 1188.11039 Granville, A.; Soundararajan, K. 2 2004 The number of unsieved integers up to \(x\). Zbl 1055.11057 Granville, Andrew; Soundararajan, K. 1 2004 The distribution of values of \(L(1,\chi_d)\). Zbl 1044.11080 Granville, Andrew; Soundararajan, K. 73 2003 Decay of mean values of multiplicative functions. Zbl 1047.11093 Granville, Andrew; Soundararajan, K. 25 2003 The number of fields generated by the square root of values of a given polynomial. Zbl 1044.11087 Cutter, Pamela; Granville, Andrew; Tucker, Thomas J. 6 2003 It’s as easy as \(abc\). Zbl 1160.11318 Granville, Andrew; Tucker, Thomas J. 29 2002 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067 Granville, Andrew; Pomerance, Carl 15 2002 Upper bounds for \(|L(1,\chi)|\). Zbl 1022.11041 Granville, Andrew; Soundararajan, K. 14 2002 On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005 Cai, Tianxin; Granville, Andrew 10 2002 Unit fractions and the class number of a cyclotomic field. Zbl 1056.11059 Croot, Ernest S. III; Granville, Andrew 2 2002 Product of integers in an interval, modulo squares. Zbl 1107.11042 Granville, Andrew; Selfridge, J. L. 1 2002 Large character sums. Zbl 0983.11053 Granville, Andrew; Soundararajan, K. 47 2001 The spectrum of multiplicative functions. Zbl 1036.11042 Granville, Andrew; Soundararajan, K. 18 2001 More points than expected on curves over finite field extensions. Zbl 1023.11029 Brock, Bradley W.; Granville, Andrew 13 2001 \(ABC\) implies no “Siegel zeros” for \(L\)-functions of characters with negative discriminant. Zbl 0967.11033 Granville, Andrew; Stark, H. M. 21 2000 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092 Granville, Andrew; Mollin, R. A.; Williams, H. C. 5 2000 Rabinowitsch revisited. Zbl 0985.11040 Granville, Andrew; Mollin, Richard A. 4 2000 The least common multiple and lattice points on hyperbolas. Zbl 0983.11058 Granville, Andrew; Jiménez-Urroz, Jorge 3 2000 Borwein and Bradley’s Apéry-like formulae for \(\zeta(4n+3)\). Zbl 0976.11035 Almkvist, Gert; Granville, Andrew 15 1999 The set of differences of a given set. Zbl 0983.05077 Granville, Andrew; Roesler, Friedrich 3 1999 On the scarcity of powerful binomial coefficients. Zbl 1033.11007 Granville, Andrew 2 1999 ...and 60 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,808 Authors 54 Shparlinski, Igor E. 43 Granville, Andrew James 29 Luca, Florian 27 Soundararajan, Kannan 21 Banks, William David 19 Lamzouri, Youness 19 Pollack, Paul 18 Pomerance, Carl Bernard 15 Matomäki, Kaisa 14 Ford, Kevin B. 14 Sun, Zhi-Wei 13 Radziwiłł, Maksym 13 Tao, Terence 13 Tenenbaum, Gérald 12 Mangerel, Alexander P. 12 Moree, Pieter 11 Zaharescu, Alexandru 10 Harper, Adam J. 10 Konyagin, Sergeĭ Vladimirovich 10 Ramaré, Olivier 9 Bennett, Michael A. 9 Eie, Minking 9 Pan, Hao 9 Shao, Xuancheng 9 Teräväinen, Joni 8 Drappeau, Sary 8 Friedlander, John Benjamin 8 Gorodetsky, Ofir 8 Maynard, James 8 Meštrović, Romeo 8 Wu, Jie 8 Zhang, Zhenxiang 7 Bradley, David M. 7 Cilleruelo, Javier 7 Croot, Ernie 7 de la Bretèche, Régis 7 Erdélyi, Tamás 7 Hajdu, Lajos 7 Klurman, Oleksiy 7 Lagarias, Jeffrey C. 7 Munsch, Marc 7 Ohno, Yasuo 7 Ono, Ken 7 Sofos, Efthymios 7 Stănică, Pantelimon 7 Wigman, Igor 6 Aymone, Marco 6 Baruah, Nayandeep Deka 6 Bourgain, Jean 6 Chen, Kwang-Wu 6 De Koninck, Jean-Marie 6 Elsholtz, Christian 6 Freiberg, Tristan 6 Goldmakher, Leo 6 Hoffman, Michael E. 6 Ji, Lijun 6 Koparal, Sibel 6 Koukoulopoulos, Dimitris 6 Kowalski, Emmanuel 6 Lengyel, Tamás 6 Martin, Greg 6 Navarro Ortega, Gabriel 6 Omur, Nese 6 Ostafe, Alina 6 Poonen, Bjorn 6 Roy, Akash Singha 6 Rudnick, Zeév 6 Silverman, Joseph Hillel 6 Tong-Viet, Hung P. 6 Vatwani, Akshaa 6 Winterhof, Arne 5 Alkan, Emre 5 Bhowmik, Gautami 5 Borwein, Peter Benjamin 5 Chen, Yonggao 5 David, Chantal 5 Devin, Lucile 5 Dietmann, Rainer 5 Dilcher, Karl 5 Du, Xiaoni 5 Fiorilli, Daniel 5 Freitas, Nuno 5 Grantham, Jon 5 Kerr, Bryce 5 Kurlberg, Pär 5 Lau, Yuk-Kam 5 Lemke Oliver, Robert J. 5 Louboutin, Stéphane R. 5 Marinucci, Domenico 5 McNew, Nathan 5 Moshe, Yossi 5 Poly, Guillaume 5 Richter, Florian Karl 5 Sun, Zhihong 5 Tauraso, Roberto 5 Tengely, Szabolcs 5 Tucker, Thomas John 5 Wagstaff, Samuel Standfield jun. 5 Zhang, Wenpeng 4 Aistleitner, Christoph ...and 1,708 more Authors all top 5 Cited in 276 Serials 199 Journal of Number Theory 78 International Journal of Number Theory 62 Mathematics of Computation 45 Proceedings of the American Mathematical Society 44 The Ramanujan Journal 41 Mathematika 37 Transactions of the American Mathematical Society 35 Integers 34 Discrete Mathematics 33 Acta Arithmetica 29 Mathematical Proceedings of the Cambridge Philosophical Society 27 Journal of Algebra 24 Journal de Théorie des Nombres de Bordeaux 23 Mathematische Annalen 21 Bulletin of the Australian Mathematical Society 20 Advances in Mathematics 19 Functiones et Approximatio. Commentarii Mathematici 19 Monatshefte für Mathematik 17 Bulletin of the London Mathematical Society 17 Experimental Mathematics 16 Archiv der Mathematik 16 Compositio Mathematica 16 Finite Fields and their Applications 15 Journal of Mathematical Analysis and Applications 15 Journal of Combinatorial Theory. Series A 15 Bulletin of the American Mathematical Society. New Series 14 Israel Journal of Mathematics 14 Journal of the London Mathematical Society. Second Series 13 Mathematische Zeitschrift 13 Indagationes Mathematicae. New Series 12 American Mathematical Monthly 12 Journal d’Analyse Mathématique 12 Rocky Mountain Journal of Mathematics 12 Canadian Mathematical Bulletin 12 Designs, Codes and Cryptography 12 Annals of Mathematics. Second Series 12 Journal of the European Mathematical Society (JEMS) 12 Algebra & Number Theory 12 Research in Number Theory 10 Duke Mathematical Journal 10 Acta Mathematica Hungarica 10 Journal of the Australian Mathematical Society 10 Science China. Mathematics 9 Mathematical Notes 9 The Electronic Journal of Combinatorics 9 Journal of Integer Sequences 9 Mediterranean Journal of Mathematics 8 Communications in Algebra 8 Czechoslovak Mathematical Journal 8 Inventiones Mathematicae 8 Michigan Mathematical Journal 8 Proceedings of the London Mathematical Society. Third Series 8 Geometric and Functional Analysis. GAFA 8 Forum of Mathematics, Sigma 8 Discrete Analysis 7 Discrete Applied Mathematics 7 Journal für die Reine und Angewandte Mathematik 7 Revista Matemática Iberoamericana 7 Journal of the American Mathematical Society 7 Electronic Journal of Probability 7 Acta Mathematica Sinica. English Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Complexity 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 6 Expositiones Mathematicae 6 Research in the Mathematical Sciences 5 Lithuanian Mathematical Journal 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Annales de l’Institut Fourier 5 Canadian Journal of Mathematics 5 Colloquium Mathematicum 5 Journal of Pure and Applied Algebra 5 Nagoya Mathematical Journal 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Journal of Combinatorial Designs 5 Journal of Group Theory 5 Oberwolfach Reports 4 Information Processing Letters 4 Periodica Mathematica Hungarica 4 The Mathematical Intelligencer 4 The Fibonacci Quarterly 4 Journal of the Mathematical Society of Japan 4 Pacific Journal of Mathematics 4 Theoretical Computer Science 4 European Journal of Combinatorics 4 Journal of Symbolic Computation 4 Aequationes Mathematicae 4 Elemente der Mathematik 4 Stochastic Processes and their Applications 4 Turkish Journal of Mathematics 4 Annals of Combinatorics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Journal of the Institute of Mathematics of Jussieu 4 Journal of Statistical Mechanics: Theory and Experiment 3 Communications in Mathematical Physics 3 Indian Journal of Pure & Applied Mathematics 3 Linear and Multilinear Algebra 3 Illinois Journal of Mathematics 3 Journal of Functional Analysis 3 Proceedings of the Edinburgh Mathematical Society. Series II ...and 176 more Serials all top 5 Cited in 49 Fields 1,511 Number theory (11-XX) 245 Combinatorics (05-XX) 114 Algebraic geometry (14-XX) 102 Group theory and generalizations (20-XX) 92 Probability theory and stochastic processes (60-XX) 52 Dynamical systems and ergodic theory (37-XX) 47 Information and communication theory, circuits (94-XX) 43 Computer science (68-XX) 38 Functions of a complex variable (30-XX) 36 Special functions (33-XX) 31 Field theory and polynomials (12-XX) 28 Commutative algebra (13-XX) 22 Global analysis, analysis on manifolds (58-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 15 Associative rings and algebras (16-XX) 14 Convex and discrete geometry (52-XX) 12 Partial differential equations (35-XX) 12 Numerical analysis (65-XX) 10 Sequences, series, summability (40-XX) 9 Real functions (26-XX) 9 Ordinary differential equations (34-XX) 9 Differential geometry (53-XX) 8 Measure and integration (28-XX) 7 General and overarching topics; collections (00-XX) 7 History and biography (01-XX) 7 Mathematical logic and foundations (03-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Approximations and expansions (41-XX) 6 Quantum theory (81-XX) 5 Manifolds and cell complexes (57-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Nonassociative rings and algebras (17-XX) 4 Topological groups, Lie groups (22-XX) 4 Geometry (51-XX) 4 Statistics (62-XX) 3 Potential theory (31-XX) 3 Algebraic topology (55-XX) 3 Mathematics education (97-XX) 2 Category theory; homological algebra (18-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 General algebraic systems (08-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.