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 Documents Indexed: 173 Publications since 1985, including 3 Books 4 Contributions as Editor · 1 Further Contribution Reviewing Activity: 56 Reviews Biographic References: 1 Publication Co-Authors: 114 Co-Authors with 115 Joint Publications 3,832 Co-Co-Authors all top 5 Co-Authors 62 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 2 Alford, William Robert 2 Balog, Antal 2 Cilleruelo, Javier 2 Croot, Ernie 2 de la Bretèche, Régis 2 Erdős, Pál 2 Martin, Greg 2 Mollin, Richard Anthony 2 Pemantle, Robin 2 Shallit, Jeffrey Outlaw 2 Tetali, Prasad 2 Tucker, Thomas John 2 Wigman, Igor 2 Williams, Hugh Cowie 1 Abrams, Aaron 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 Fung, Gilbert W. 1 Goldmakher, Leo 1 Goulden, Ian P. 1 Granville, Jennifer 1 Gronau, Hans-Dietrich O. F. 1 Hartman, Alan 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 Lamzouri, Youness 1 Lemke Oliver, Robert J. 1 Li, Shuguang 1 Luca, Florian 1 Lumley, Allysa 1 Maier, Helmut 1 Matomäki, Kaisa Sofia 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 1 Powell, Barry J. 1 Ramaré, Olivier 1 Richmond, L. Bruce 1 Roesler, Friedrich 1 Rogers, Nicholas F. 1 Schinzel, Andrzej 1 Selfridge, John L. 1 Shakan, George 1 Shank, Herbert S. 1 Shiu, Daniel 1 Shiu, Peter 1 Shparlinski, Igor E. ...and 16 more Co-Authors all top 5 Serials 9 American Mathematical Monthly 6 Acta Arithmetica 5 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 Bulletin of the American Mathematical Society. New Series 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 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Scandinavian Actuarial Journal 1 Journal of Sichuan University. Natural Science Edition 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 all top 5 Fields 165 Number theory (11-XX) 22 Combinatorics (05-XX) 6 General and overarching topics; collections (00-XX) 6 Algebraic geometry (14-XX) 5 History and biography (01-XX) 5 Field theory and polynomials (12-XX) 4 Computer science (68-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 149 Publications have been cited 1,819 times in 1,533 Documents Cited by ▼ Year ▼ Arithmetic properties of binomial coefficients. I: Binomial coefficients modulo prime powers. Zbl 0903.11005Granville, Andrew 121 1997 There are infinitely many Carmichael numbers. Zbl 0816.11005Alford, W. R.; Granville, Andrew; Pomerance, Carl 116 1994 Defect zero \(p\)-blocks for finite simple groups. Zbl 0855.20007Granville, Andrew; Ono, Ken 113 1996 On the equations \(z^ m = F(x,y)\) and \(Ax^ p + By^ q = Cz^ r\). Zbl 0838.11023Darmon, Henri; Granville, Andrew 90 1995 The distribution of values of \(L(1,\chi_d)\). Zbl 1044.11080Granville, Andrew; Soundararajan, K. 66 2003 A decomposition of Riemann’s zeta-function. Zbl 0907.11024Granville, Andrew 64 1997 \(abc\) allows us to count squarefrees. Zbl 0924.11018Granville, Andrew 59 1998 Smooth numbers: computational number theory and beyond. Zbl 1230.11157Granville, Andrew 58 2008 Large character sums: pretentious characters and the Pólya-Vinogradov theorem. Zbl 1210.11090Granville, Andrew; Soundararajan, K. 58 2007 Harald Cramér and the distribution of prime numbers. Zbl 0833.01018Granville, Andrew 44 1995 Large character sums. Zbl 0983.11053Granville, Andrew; Soundararajan, K. 39 2001 Prime number races. Zbl 1139.11037Granville, Andrew; Martin, Greg 30 2006 Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Zbl 0868.11009Granville, Andrew; Ramaré, Olivier 28 1996 The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042Granville, Andrew; Wigman, Igor 27 2011 Limitations to the equi-distribution of primes. I. Zbl 0671.10041Friedlander, John; Granville, Andrew 24 1989 It’s as easy as \(abc\). Zbl 1160.11318Granville, Andrew; Tucker, Thomas J. 23 2002 Sieving and the Erdős-Kac theorem. Zbl 1145.11071Granville, Andrew; Soundararajan, K. 22 2007 Extreme values of \(|\zeta(1+it)|\). Zbl 1131.11055Granville, Andrew; Soundararajan, K. 22 2006 \(ABC\) implies no “Siegel zeros” for \(L\)-functions of characters with negative discriminant. Zbl 0967.11033Granville, Andrew; Stark, H. M. 21 2000 Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012Kamienny, S.; Mazur, B. 20 1995 Decay of mean values of multiplicative functions. Zbl 1047.11093Granville, Andrew; Soundararajan, K. 20 2003 Zeros of Fekete polynomials. Zbl 1007.11053Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Unexpected irregularities in the distribution of prime numbers. Zbl 0843.11043Granville, Andrew 18 1995 The spectrum of multiplicative functions. Zbl 1036.11042Granville, Andrew; Soundararajan, K. 17 2001 Primes in intervals of bounded length. Zbl 1319.11064Granville, Andrew 17 2015 Prime factors of dynamical sequences. Zbl 1290.11019Faber, Xander; Granville, Andrew 17 2011 Squares in arithmetic progressions. Zbl 0771.11034Bombieri, Enrico; Granville, Andrew; Pintz, János 16 1992 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 16 2005 Borwein and Bradley’s Apéry-like formulae for \(\zeta(4n+3)\). Zbl 0976.11035Almkvist, Gert; Granville, Andrew 15 1999 Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058Cilleruelo, Javier; Granville, Andrew 14 2007 Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032Granville, Andrew; Soundararajan, Kannan 14 2008 Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012Granville, Andrew; Wigman, Igor 14 2017 The square of the Fermat quotient. Zbl 1083.11005Granville, Andrew 13 2004 Subdesigns in Steiner quadruple systems. Zbl 0726.05017Granville, Andrew; Hartman, Alan 13 1991 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 12 2002 On the difficulty of finding reliable witnesses. Zbl 0828.11074Alford, W. R.; Granville, Andrew; Pomerance, Carl 12 1994 Values of Bernoulli polynomials. Zbl 0856.11008Granville, Andrew; Sun, Zhi-Wei 12 1996 Integers, without large prime factors, in arithmetic progressions. I. Zbl 0784.11045Granville, Andrew 12 1993 Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028Granville, Andrew 12 2007 Multiplicative functions in arithmetic progressions. Zbl 1306.11078Balog, Antal; Granville, Andrew; Soundararajan, Kannan 11 2013 Upper bounds for \(|L(1,\chi)|\). Zbl 1022.11041Granville, Andrew; Soundararajan, K. 11 2002 On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C. 11 1990 Zaphod Beeblebrox’s brain and the fifty-ninth row of Pascal’s triangle. Zbl 0757.05003Granville, Andrew 10 1992 When the sieve works. Zbl 1326.11055Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa 10 2015 Some conjectures related to Fermat’s Last Theorem. Zbl 0702.11015Granville, Andrew 10 1990 Oscillation theorems for primes in arithmetic progressions and for sifting functions. Zbl 0724.11040Friedlander, John; Granville, Andrew; Hildebrand, Adolf; Maier, Helmut 10 1991 Estimates for representation numbers of quadratic forms. Zbl 1135.11020Blomer, Valentin; Granville, Andrew 10 2006 The first case of Fermat’s last theorem is true for all prime exponents up to \(714,591,416,091,389\). Zbl 0645.10018Granville, Andrew; Monagan, Michael B. 10 1988 Bombieri-Vinogradov for multiplicative functions, and beyond the \(x^{1/2}\)-barrier. Zbl 1473.11185Granville, Andrew; Shao, Xuancheng 10 2019 A new proof of Halász’s theorem, and its consequences. Zbl 1443.11200Granville, Andrew; Harper, Adam J.; Soundararajan, K. 10 2019 Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123Granville, Andrew 9 2007 More points than expected on curves over finite field extensions. Zbl 1023.11029Brock, Bradley W.; Granville, Andrew 9 2001 On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005Cai, Tianxin; Granville, Andrew 9 2002 Nested Steiner n-cycle systems and perpendicular arrays. Zbl 0732.05006Granville, A.; Moisiadis, A.; Rees, R. 9 1988 Integers, without large prime factors, in arithmetic progressions. II. Zbl 0792.11036Granville, Andrew 9 1993 Prime divisors are Poisson distributed. Zbl 1118.11005Granville, Andrew 9 2007 The frequency and the structure of large character sums. Zbl 1409.11079Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris 8 2018 Big biases amongst products of two primes. Zbl 1347.11067Dummit, David; Granville, Andrew; Kisilevsky, Hershy 8 2016 An uncertainty principle for arithmetic sequences. Zbl 1139.11040Granville, Andrew; Soundararajan, K. 8 2007 On the exponential sum over \(k\)-free numbers. Zbl 0922.11071Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D. 8 1998 On pairs of coprime integers with no large prime factors. Zbl 0745.11043Granville, Andrew 7 1991 On complementary decompositions of the complete graph. Zbl 0674.05050Granville, Andrew; Moisiadis, Alexandros; Rees, Rolf 7 1989 On the size of the first factor of the class number of a cyclotomic field. Zbl 0701.11051Granville, A. 7 1990 Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001Granville, Andrew 7 2006 Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej 7 2008 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 6 1992 Corrigendum to “Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis”. Zbl 1235.11092Granville, Andrew 6 2008 Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109Granville, Andrew; Kurlberg, Pär 6 2008 The number of sumsets in a finite field. Zbl 1223.11028Alon, Noga; Granville, Andrew; Ubis, Adrián 6 2010 On the least prime in certain arithmetic progression. Zbl 0658.10049Granville, Andrew; Pomerance, Carl 6 1990 It is easy to determine whether a given integer is prime. Zbl 1110.11002Granville, Andrew 6 2005 Different approaches to the distribution of primes. Zbl 1275.11129Granville, Andrew 6 2010 A binary additive problem of Erdős and the order of \(2 \bmod {p^2}\). Zbl 0912.11003Granville, Andrew; Soundararajan, K. 6 1998 Large character sums: Burgess’s theorem and zeros of \(L\)-functions. Zbl 1444.11177Granville, Andrew; Soundararajan, Kannan 6 2018 Smooth-supported multiplicative functions in arithmetic progressions beyond the \(x^{1/2}\)-barrier. Zbl 1428.11174Drappeau, Sary; Granville, Andrew; Shao, Xuancheng 6 2017 On sharp transitions in making squares. Zbl 1321.11122Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad 6 2012 The prime factors of Wendt’s binomial circulant determinant. Zbl 0767.11059Fee, Greg; Granville, Andrew 5 1991 On a paper of Agur, Fraenkel and Klein. Zbl 0755.05005Granville, Andrew 5 1991 Visibility in the plane. Zbl 1176.11027Adhikari, Sukumar Das; Granville, Andrew 5 2009 Aurifeuillian factorization. Zbl 1107.11050Granville, Andrew; Pleasants, Peter 5 2006 Checking the Goldbach conjecture on a vector computer. Zbl 0679.10002Granville, A.; Van de Lune, J.; te Riele, H. J. J. 5 1989 Powerful numbers and Fermat’s Last Theorem. Zbl 0595.10011Granville, Andrew 5 1986 Representing binomial coefficients as sums of squares. Zbl 0717.11016Granville, Andrew; Zhu, Yiliang 5 1990 Smoothing ‘smooth’ numbers. Zbl 0795.11041Friedlander, John B.; Granville, Andrew 5 1993 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092Granville, Andrew; Mollin, R. A.; Williams, H. C. 5 2000 The Frobenius postage stamp problem, and beyond. Zbl 07301143Granville, A.; Shakan, G. 5 2020 Prime suspects. The anatomy of integers and permutations. Illustrated by Robert J. Lewis. Zbl 1423.00004Granville, Andrew; Granville, Jennifer 5 2019 When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105Granville, Andrew; Shao, Xuancheng 5 2018 The number of fields generated by the square root of values of a given polynomial. Zbl 1044.11087Cutter, Pamela; Granville, Andrew; Tucker, Thomas J. 5 2003 Sum-product formulae. Zbl 1407.11043Granville, Andrew; Solymosi, József 5 2016 Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011Balog, Antal; Granville, Andrew; Solymosi, Jozsef 5 2017 Zeta functions for ideal classes in real quadratic fields, at \(s=0\). Zbl 1276.11180Biró, András; Granville, Andrew 5 2012 Limitations to the equi-distribution of primes. IV. Zbl 0736.11049Friedlander, John; Granville, Andrew 4 1991 Squares in arithmetic progressions and infinitely many primes. Zbl 1391.11115Granville, Andrew 4 2017 Uniform distribution. Zbl 1142.11054Granville, Andrew; Rudnick, Zeév 4 2007 The distribution of roots of a polynomial. Zbl 1170.11016Granville, Andrew 4 2007 Best possible densities of Dickson \(m\)-tuples, as a consequence of Zhang-Maynard-Tao. Zbl 1391.11116Granville, Andrew; Kane, Daniel M.; Koukoulopoulos, Dimitris; Oliver, Robert J. Lemke 4 2015 Mean values of multiplicative functions over function fields. Zbl 1394.11069Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 4 2015 Ranks of quadratic twists of elliptic curves. Zbl 1365.11070Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F. 4 2014 Bounding the coefficients of a divisor of a given polynomial. Zbl 0713.12001Granville, Andrew 4 1990 Primes in short intervals: heuristics and calculations. Zbl 07708950Granville, Andrew; Lumley, Allysa 1 2023 Consecutive real quadratic fields with large class numbers. Zbl 07726859Cherubini, Giacomo; Fazzari, Alessandro; Granville, Andrew; Kala, Vítězslav; Yatsyna, Pavlo 1 2023 Sieving intervals and Siegel zeros. Zbl 1504.11089Granville, Andrew 1 2022 A tight structure theorem for sumsets. Zbl 1496.11048Granville, Andrew; Walker, Aled 4 2021 The Frobenius postage stamp problem, and beyond. Zbl 07301143Granville, A.; Shakan, G. 5 2020 Bombieri-Vinogradov for multiplicative functions, and beyond the \(x^{1/2}\)-barrier. Zbl 1473.11185Granville, Andrew; Shao, Xuancheng 10 2019 A new proof of Halász’s theorem, and its consequences. Zbl 1443.11200Granville, Andrew; Harper, Adam J.; Soundararajan, K. 10 2019 Prime suspects. The anatomy of integers and permutations. Illustrated by Robert J. Lewis. Zbl 1423.00004Granville, Andrew; Granville, Jennifer 5 2019 Beyond the LSD method for the partial sums of multiplicative functions. Zbl 1455.11128Granville, Andrew; Koukoulopoulos, Dimitris 2 2019 Natural exact covering systems and the reversion of the Möbius series. Zbl 1427.05022Goulden, I. P.; Granville, Andrew; Richmond, L. Bruce; Shallit, Jeffrey 1 2019 Number theory revealed: an introduction. Zbl 1454.11001Granville, Andrew 1 2019 The frequency and the structure of large character sums. Zbl 1409.11079Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris 8 2018 Large character sums: Burgess’s theorem and zeros of \(L\)-functions. Zbl 1444.11177Granville, Andrew; Soundararajan, Kannan 6 2018 When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105Granville, Andrew; Shao, Xuancheng 5 2018 A more intuitive proof of a sharp version of Halász’s theorem. Zbl 1456.11182Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 3 2018 Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012Granville, Andrew; Wigman, Igor 14 2017 Smooth-supported multiplicative functions in arithmetic progressions beyond the \(x^{1/2}\)-barrier. Zbl 1428.11174Drappeau, Sary; Granville, Andrew; Shao, Xuancheng 6 2017 Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011Balog, Antal; Granville, Andrew; Solymosi, Jozsef 5 2017 Squares in arithmetic progressions and infinitely many primes. Zbl 1391.11115Granville, Andrew 4 2017 Big biases amongst products of two primes. Zbl 1347.11067Dummit, David; Granville, Andrew; Kisilevsky, Hershy 8 2016 Sum-product formulae. Zbl 1407.11043Granville, Andrew; Solymosi, József 5 2016 Primes in intervals of bounded length. Zbl 1319.11064Granville, Andrew 17 2015 When the sieve works. Zbl 1326.11055Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa 10 2015 Best possible densities of Dickson \(m\)-tuples, as a consequence of Zhang-Maynard-Tao. Zbl 1391.11116Granville, Andrew; Kane, Daniel M.; Koukoulopoulos, Dimitris; Oliver, Robert J. Lemke 4 2015 Mean values of multiplicative functions over function fields. Zbl 1394.11069Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan 4 2015 About the cover: a new mathematical celebrity. Zbl 1310.01017Granville, Andrew 1 2015 Ranks of quadratic twists of elliptic curves. Zbl 1365.11070Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F. 4 2014 Friable density. (Densité des friables.) Zbl 1318.11121de la Bretèche, Régis; Granville, Andrew 3 2014 Multiplicative functions in arithmetic progressions. Zbl 1306.11078Balog, Antal; Granville, Andrew; Soundararajan, Kannan 11 2013 On sharp transitions in making squares. Zbl 1321.11122Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad 6 2012 Zeta functions for ideal classes in real quadratic fields, at \(s=0\). Zbl 1276.11180Biró, András; Granville, Andrew 5 2012 Primitive prime factors in second-order linear recurrence sequences. Zbl 1272.11027Granville, Andrew 1 2012 The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042Granville, Andrew; Wigman, Igor 27 2011 Prime factors of dynamical sequences. Zbl 1290.11019Faber, Xander; Granville, Andrew 17 2011 The number of sumsets in a finite field. Zbl 1223.11028Alon, Noga; Granville, Andrew; Ubis, Adrián 6 2010 Different approaches to the distribution of primes. Zbl 1275.11129Granville, Andrew 6 2010 Visibility in the plane. Zbl 1176.11027Adhikari, Sukumar Das; Granville, Andrew 5 2009 Pretentiousness in analytic number theory. Zbl 1236.11086Granville, Andrew 3 2009 Close lattice points on circles. Zbl 1229.11124Cilleruelo, Javier; Granville, Andrew 3 2009 Smooth numbers: computational number theory and beyond. Zbl 1230.11157Granville, Andrew 58 2008 Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032Granville, Andrew; Soundararajan, Kannan 14 2008 Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej 7 2008 Corrigendum to “Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis”. Zbl 1235.11092Granville, Andrew 6 2008 Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109Granville, Andrew; Kurlberg, Pär 6 2008 Prime number patterns. Zbl 1145.11069Granville, Andrew 2 2008 Running time predictions for factoring algorithms. Zbl 1205.11132Croot, 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 1210.11090Granville, Andrew; Soundararajan, K. 58 2007 Sieving and the Erdős-Kac theorem. Zbl 1145.11071Granville, Andrew; Soundararajan, K. 22 2007 Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058Cilleruelo, Javier; Granville, Andrew 14 2007 Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028Granville, Andrew 12 2007 Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123Granville, Andrew 9 2007 Prime divisors are Poisson distributed. Zbl 1118.11005Granville, Andrew 9 2007 An uncertainty principle for arithmetic sequences. Zbl 1139.11040Granville, Andrew; Soundararajan, K. 8 2007 Uniform distribution. Zbl 1142.11054Granville, Andrew; Rudnick, Zeév 4 2007 The distribution of roots of a polynomial. Zbl 1170.11016Granville, Andrew 4 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 4 2007 An introduction to additive combinatorics. Zbl 1183.11007Granville, Andrew 3 2007 Torsion points on curves. Zbl 1172.11020Granville, Andrew; Rudnick, Zeév 3 2007 Erratum: Prime divisors are Poisson distributed. Zbl 1234.11126Granville, Andrew 3 2007 Negative values of truncations to \(L(1,\chi)\). Zbl 1214.11093Granville, Andrew; Soundararajan, K. 3 2007 Prime number races. Zbl 1139.11037Granville, Andrew; Martin, Greg 30 2006 Extreme values of \(|\zeta(1+it)|\). Zbl 1131.11055Granville, Andrew; Soundararajan, K. 22 2006 Estimates for representation numbers of quadratic forms. Zbl 1135.11020Blomer, Valentin; Granville, Andrew 10 2006 Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001Granville, Andrew 7 2006 Aurifeuillian factorization. Zbl 1107.11050Granville, Andrew; Pleasants, Peter 5 2006 Residue races. Zbl 1161.11300Granville, Andrew; Shiu, Daniel; Shiu, Peter 2 2006 On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races. Zbl 1068.11043Granville, Andrew; Shparlinski, Igor E.; Zaharescu, Alexandru 16 2005 It is easy to determine whether a given integer is prime. Zbl 1110.11002Granville, Andrew 6 2005 Prime number races. Zbl 1358.11139Granville, Andrew; Martin, Greg 1 2005 The square of the Fermat quotient. Zbl 1083.11005Granville, Andrew 13 2004 Errata to: The distribution of values of \(L(1,\chi_d)\). Zbl 1188.11039Granville, A.; Soundararajan, K. 2 2004 The number of unsieved integers up to \(x\). Zbl 1055.11057Granville, Andrew; Soundararajan, K. 1 2004 The distribution of values of \(L(1,\chi_d)\). Zbl 1044.11080Granville, Andrew; Soundararajan, K. 66 2003 Decay of mean values of multiplicative functions. Zbl 1047.11093Granville, Andrew; Soundararajan, K. 20 2003 The number of fields generated by the square root of values of a given polynomial. Zbl 1044.11087Cutter, Pamela; Granville, Andrew; Tucker, Thomas J. 5 2003 It’s as easy as \(abc\). Zbl 1160.11318Granville, Andrew; Tucker, Thomas J. 23 2002 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 12 2002 Upper bounds for \(|L(1,\chi)|\). Zbl 1022.11041Granville, Andrew; Soundararajan, K. 11 2002 On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005Cai, Tianxin; Granville, Andrew 9 2002 Unit fractions and the class number of a cyclotomic field. Zbl 1056.11059Croot, Ernest S. III; Granville, Andrew 1 2002 Large character sums. Zbl 0983.11053Granville, Andrew; Soundararajan, K. 39 2001 The spectrum of multiplicative functions. Zbl 1036.11042Granville, Andrew; Soundararajan, K. 17 2001 More points than expected on curves over finite field extensions. Zbl 1023.11029Brock, Bradley W.; Granville, Andrew 9 2001 \(ABC\) implies no “Siegel zeros” for \(L\)-functions of characters with negative discriminant. Zbl 0967.11033Granville, Andrew; Stark, H. M. 21 2000 Zeros of Fekete polynomials. Zbl 1007.11053Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092Granville, Andrew; Mollin, R. A.; Williams, H. C. 5 2000 The least common multiple and lattice points on hyperbolas. Zbl 0983.11058Granville, Andrew; Jiménez-Urroz, Jorge 3 2000 Rabinowitsch revisited. Zbl 0985.11040Granville, Andrew; Mollin, Richard A. 3 2000 Borwein and Bradley’s Apéry-like formulae for \(\zeta(4n+3)\). Zbl 0976.11035Almkvist, Gert; Granville, Andrew 15 1999 The set of differences of a given set. Zbl 0983.05077Granville, Andrew; Roesler, Friedrich 3 1999 On the scarcity of powerful binomial coefficients. Zbl 1033.11007Granville, Andrew 2 1999 Motivating the multiplicative spectrum. Zbl 0935.11033Granville, Andrew; Soundararajan, K. 1 1999 \(abc\) allows us to count squarefrees. Zbl 0924.11018Granville, Andrew 59 1998 On the exponential sum over \(k\)-free numbers. Zbl 0922.11071Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D. 8 1998 A binary additive problem of Erdős and the order of \(2 \bmod {p^2}\). Zbl 0912.11003Granville, Andrew; Soundararajan, K. 6 1998 Arithmetic properties of binomial coefficients. I: Binomial coefficients modulo prime powers. Zbl 0903.11005Granville, Andrew 121 1997 A decomposition of Riemann’s zeta-function. Zbl 0907.11024Granville, Andrew 64 1997 Correction to: Zaphod Beeblebrox’s brain and the fifty-ninth row of Pascal’s triangle. Zbl 0889.05004Granville, Andrew 1 1997 Defect zero \(p\)-blocks for finite simple groups. Zbl 0855.20007Granville, Andrew; Ono, Ken 113 1996 ...and 49 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,578 Authors 47 Shparlinski, Igor E. 39 Granville, Andrew James 26 Luca, Florian 25 Soundararajan, Kannan 21 Banks, William David 17 Lamzouri, Youness 16 Pomerance, Carl Bernard 14 Ford, Kevin B. 14 Matomäki, Kaisa Sofia 14 Pollack, Paul 14 Sun, Zhi-Wei 12 Radziwiłł, Maksym 12 Tao, Terence 12 Tenenbaum, Gérald 11 Moree, Pieter 10 Harper, Adam J. 10 Zaharescu, Alexandru 9 Bennett, Michael A. 9 Pan, Hao 9 Ramaré, Olivier 9 Shao, Xuancheng 8 Konyagin, Sergeĭ Vladimirovich 8 Meštrović, Romeo 8 Wu, Jie 8 Zhang, Zhenxiang 7 Bradley, David M. 7 Cilleruelo, Javier 7 Drappeau, Sary 7 Eie, Minking 7 Erdélyi, Tamás 7 Hajdu, Lajos 7 Mangerel, Alexander P. 7 Maynard, James 7 Ohno, Yasuo 7 Stănică, Pantelimon 7 Teräväinen, Joni 7 Wigman, Igor 6 Aymone, Marco 6 Bourgain, Jean 6 Croot, Ernie 6 De Koninck, Jean-Marie 6 de la Bretèche, Régis 6 Elsholtz, Christian 6 Freiberg, Tristan 6 Friedlander, John Benjamin 6 Goldmakher, Leo 6 Hoffman, Michael E. 6 Ji, Lijun 6 Klurman, Oleksiy 6 Koukoulopoulos, Dimitris 6 Lengyel, Tamás 6 Martin, Greg 6 Munsch, Marc 6 Ono, Ken 6 Ostafe, Alina 6 Poonen, Bjorn 6 Rudnick, Zeév 6 Silverman, Joseph Hillel 6 Sofos, Efthymios 6 Winterhof, Arne 5 Alkan, Emre 5 Baruah, Nayandeep Deka 5 Bhowmik, Gautami 5 Borwein, Peter Benjamin 5 Chen, Kwang-Wu 5 Chen, Yonggao 5 Dietmann, Rainer 5 Dilcher, Karl 5 Freitas, Nuno 5 Grantham, Jon 5 Koparal, Sibel 5 Kowalski, Emmanuel 5 Lagarias, Jeffrey C. 5 Lau, Yuk-Kam 5 Lemke Oliver, Robert J. 5 Moshe, Yossi 5 Navarro, Gabriel 5 Omur, Nese 5 Poly, Guillaume 5 Sun, Zhihong 5 Tauraso, Roberto 5 Tengely, Szabolcs 5 Tong-Viet, Hung P. 5 Tucker, Thomas John 5 Vatwani, Akshaa 5 Zhang, Wenpeng 4 Aistleitner, Christoph 4 Bary-Soroker, Lior 4 Cai, Tianxin 4 Cammarota, Valentina 4 Chen, Imin 4 Chu, Wenchang 4 David, Chantal 4 Dieulefait, Luis Victor 4 Gao, Weidong 4 Genčev, Marian 4 González-Jiménez, Enrique 4 Green, Ben Joseph 4 Guo, Victor Zhenyu 4 Halupczok, Karin ...and 1,478 more Authors all top 5 Cited in 261 Serials 182 Journal of Number Theory 69 International Journal of Number Theory 60 Mathematics of Computation 42 Proceedings of the American Mathematical Society 38 Mathematika 38 The Ramanujan Journal 35 Transactions of the American Mathematical Society 30 Discrete Mathematics 27 Journal of Algebra 25 Mathematical Proceedings of the Cambridge Philosophical Society 25 Integers 24 Journal de Théorie des Nombres de Bordeaux 23 Acta Arithmetica 18 Bulletin of the Australian Mathematical Society 18 Advances in Mathematics 17 Functiones et Approximatio. Commentarii Mathematici 17 Mathematische Annalen 17 Experimental Mathematics 16 Archiv der Mathematik 16 Monatshefte für Mathematik 14 Compositio Mathematica 14 Journal of Combinatorial Theory. Series A 14 Bulletin of the American Mathematical Society. New Series 14 Finite Fields and their Applications 13 Indagationes Mathematicae. New Series 12 Israel Journal of Mathematics 12 Annals of Mathematics. Second Series 11 American Mathematical Monthly 11 Designs, Codes and Cryptography 10 Journal d’Analyse Mathématique 10 Journal of Mathematical Analysis and Applications 10 Rocky Mountain Journal of Mathematics 10 Bulletin of the London Mathematical Society 10 Canadian Mathematical Bulletin 10 Duke Mathematical Journal 10 Mathematische Zeitschrift 10 Journal of the European Mathematical Society (JEMS) 9 Algebra & Number Theory 8 Communications in Algebra 8 Czechoslovak Mathematical Journal 8 Geometric and Functional Analysis. 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Académie des Sciences, Paris 6 Journal of the American Mathematical Society 6 Journal of Integer Sequences 5 Discrete Applied Mathematics 5 Lithuanian Mathematical Journal 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Annales de l’Institut Fourier 5 Colloquium Mathematicum 5 Nagoya Mathematical Journal 5 Journal of Complexity 5 Journal of Combinatorial Designs 5 Electronic Journal of Probability 5 Journal of Group Theory 5 Research in the Mathematical Sciences 4 The Mathematical Intelligencer 4 Canadian Journal of Mathematics 4 Journal of the Mathematical Society of Japan 4 Journal of Pure and Applied Algebra 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 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Expositiones Mathematicae 4 Annals of Combinatorics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Journal of Statistical Mechanics: Theory and Experiment 4 Oberwolfach Reports 3 Communications in Mathematical Physics 3 The Fibonacci Quarterly 3 Journal of Functional Analysis 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 Graphs and Combinatorics 3 Probability Theory and Related Fields 3 SIAM Journal on Discrete Mathematics 3 Journal of Cryptology 3 Forum Mathematicum 3 International Journal of Foundations of Computer Science 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Turkish Journal of Mathematics ...and 161 more Serials all top 5 Cited in 49 Fields 1,297 Number theory (11-XX) 215 Combinatorics (05-XX) 97 Algebraic geometry (14-XX) 92 Group theory and generalizations (20-XX) 74 Probability theory and stochastic processes (60-XX) 46 Dynamical systems and ergodic theory (37-XX) 41 Information and communication theory, circuits (94-XX) 38 Computer science (68-XX) 35 Functions of a complex variable (30-XX) 32 Special functions (33-XX) 30 Field theory and polynomials (12-XX) 23 Commutative algebra (13-XX) 20 Global analysis, analysis on manifolds (58-XX) 15 Associative rings and algebras (16-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 12 Partial differential equations (35-XX) 12 Convex and discrete geometry (52-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Numerical analysis (65-XX) 9 Real functions (26-XX) 9 Ordinary differential equations (34-XX) 7 Sequences, series, summability (40-XX) 7 Differential geometry (53-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 6 Mathematical logic and foundations (03-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Quantum theory (81-XX) 5 Measure and integration (28-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Nonassociative rings and algebras (17-XX) 4 Approximations and expansions (41-XX) 4 Geometry (51-XX) 4 Manifolds and cell complexes (57-XX) 4 Statistics (62-XX) 3 Potential theory (31-XX) 3 Algebraic topology (55-XX) 2 Category theory; homological algebra (18-XX) 2 Topological groups, Lie groups (22-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) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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