# zbMATH — the first resource for mathematics

## Granville, Andrew James

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 Author ID: granville.andrew-j Published as: Granville, Andrew; Granville, A.; Granville, Andrew J. Homepage: https://dms.umontreal.ca/~andrew/ External Links: MGP · Wikidata · Google Scholar · MathOverflow · dblp · GND · IdRef · theses.fr
 Documents Indexed: 170 Publications since 1985, including 7 Books Reviewing Activity: 56 Reviews
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#### Co-Authors

 61 single-authored 21 Soundararajan, Kannan 6 Friedlander, John Benjamin 6 Pomerance, Carl Bernard 4 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 Erdős, Pál 2 Martin, Greg 2 Mollin, Richard Anthony 2 Pemantle, Robin 2 Shallit, Jeffrey O. 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 M. 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 Conrey, John Brian 1 Croot, Ernest S. III 1 Cutter, Pamela A. 1 Darmon, Henri René 1 De Koninck, Jean-Marie 1 de la Bretèche, Régis 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 H. 1 Faber, Xander 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 Kane, Daniel M. 1 Kisilevsky, Hershy 1 Kurlberg, Pär 1 Lemke Oliver, Robert J. 1 Li, Shuguang 1 Luca, Florian 1 Maier, Helmut 1 Matomäki, Kaisa Sofia 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. 1 Spiro, Claudia Alison 1 Stark, Harold M. 1 Sun, Qi 1 Sun, Zhi-Wei 1 te Riele, Herman 1 Tenenbaum, Gérald 1 Ubis, Adrián 1 van de Lune, Jan ...and 7 more Co-Authors
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#### Serials

 9 American Mathematical Monthly 5 Acta Arithmetica 5 Journal of Number Theory 5 Annals of Mathematics. Second Series 4 Mathematics of Computation 4 Mathematika 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 Journal of the American Mathematical Society 3 Bulletin of the American Mathematical Society. New Series 3 Notices of the American Mathematical Society 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 Transactions of the American Mathematical Society 2 Comptes Rendus Mathématiques de l’Académie des Sciences 2 IMRN. International Mathematics Research Notices 2 Geometric and Functional Analysis. GAFA 2 Philosophical Transactions of the Royal Society of London. Series A 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 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 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 Experimental Mathematics 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
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#### Fields

 158 Number theory (11-XX) 21 Combinatorics (05-XX) 6 General and overarching topics; collections (00-XX) 5 Field theory and polynomials (12-XX) 5 Algebraic geometry (14-XX) 4 History and biography (01-XX) 3 Computer science (68-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Probability theory and stochastic processes (60-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)

#### Citations contained in zbMATH Open

138 Publications have been cited 1,410 times in 1,214 Documents Cited by Year
Arithmetic properties of binomial coefficients. I: Binomial coefficients modulo prime powers. Zbl 0903.11005
Granville, Andrew
1997
There are infinitely many Carmichael numbers. Zbl 0816.11005
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
Defect zero $$p$$-blocks for finite simple groups. Zbl 0855.20007
Granville, Andrew; Ono, Ken
1996
On the equations $$z^ m = F(x,y)$$ and $$Ax^ p + By^ q = Cz^ r$$. Zbl 0838.11023
Darmon, Henri; Granville, Andrew
1995
The distribution of values of $$L(1,\chi_d)$$. Zbl 1044.11080
Granville, Andrew; Soundararajan, K.
2003
A decomposition of Riemann’s zeta-function. Zbl 0907.11024
Granville, Andrew
1997
Smooth numbers: computational number theory and beyond. Zbl 1230.11157
Granville, Andrew
2008
$$abc$$ allows us to count squarefrees. Zbl 0924.11018
Granville, Andrew
1998
Large character sums: pretentious characters and the Pólya-Vinogradov theorem. Zbl 1210.11090
Granville, Andrew; Soundararajan, K.
2007
Harald Cramér and the distribution of prime numbers. Zbl 0833.01018
Granville, Andrew
1995
Large character sums. Zbl 0983.11053
Granville, Andrew; Soundararajan, K.
2001
Prime number races. Zbl 1139.11037
Granville, Andrew; Martin, Greg
2006
Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Zbl 0868.11009
Granville, Andrew; Ramaré, Olivier
1996
It’s as easy as $$abc$$. Zbl 1160.11318
Granville, Andrew; Tucker, Thomas J.
2002
Limitations to the equi-distribution of primes. I. Zbl 0671.10041
Friedlander, John; Granville, Andrew
1989
Sieving and the Erdős-Kac theorem. Zbl 1145.11071
Granville, Andrew; Soundararajan, K.
2007
Decay of mean values of multiplicative functions. Zbl 1047.11093
Granville, Andrew; Soundararajan, K.
2003
The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042
Granville, Andrew; Wigman, Igor
2011
Zeros of Fekete polynomials. Zbl 1007.11053
Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K.
2000
$$ABC$$ implies no “Siegel zeros” for $$L$$-functions of characters with negative discriminant. Zbl 0967.11033
Granville, Andrew; Stark, H. M.
2000
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
2005
Prime factors of dynamical sequences. Zbl 1290.11019
Faber, Xander; Granville, Andrew
2011
Unexpected irregularities in the distribution of prime numbers. Zbl 0843.11043
Granville, Andrew
1995
The spectrum of multiplicative functions. Zbl 1036.11042
Granville, Andrew; Soundararajan, K.
2001
Squares in arithmetic progressions. Zbl 0771.11034
Bombieri, Enrico; Granville, Andrew; Pintz, János
1992
Subdesigns in Steiner quadruple systems. Zbl 0726.05017
Granville, Andrew; Hartman, Alan
1991
Borwein and Bradley’s Apéry-like formulae for $$\zeta(4n+3)$$. Zbl 0976.11035
Almkvist, Gert; Granville, Andrew
1999
Values of Bernoulli polynomials. Zbl 0856.11008
Granville, Andrew; Sun, Zhi-Wei
1996
Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058
Cilleruelo, Javier; Granville, Andrew
2007
Extreme values of $$|\zeta(1+it)|$$. Zbl 1131.11055
Granville, Andrew; Soundararajan, K.
2006
On the difficulty of finding reliable witnesses. Zbl 0828.11074
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012
Granville, Andrew; Wigman, Igor
2017
The square of the Fermat quotient. Zbl 1083.11005
Granville, Andrew
2004
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
2002
Integers, without large prime factors, in arithmetic progressions. I. Zbl 0784.11045
Granville, Andrew
1993
Zaphod Beeblebrox’s brain and the fifty-ninth row of Pascal’s triangle. Zbl 0757.05003
Granville, Andrew
1992
Nested Steiner n-cycle systems and perpendicular arrays. Zbl 0732.05006
Granville, A.; Moisiadis, A.; Rees, R.
1988
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.
1988
Some conjectures related to Fermat’s Last Theorem. Zbl 0702.11015
Granville, Andrew
1990
Oscillation theorems for primes in arithmetic progressions and for sifting functions. Zbl 0724.11040
Friedlander, John; Granville, Andrew; Hildebrand, Adolf; Maier, Helmut
1991
Primes in intervals of bounded length. Zbl 1319.11064
Granville, Andrew
2015
Multiplicative functions in arithmetic progressions. Zbl 1306.11078
Balog, Antal; Granville, Andrew; Soundararajan, Kannan
2013
On the exponential sum over $$k$$-free numbers. Zbl 0922.11071
Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D.
1998
More points than expected on curves over finite field extensions. Zbl 1023.11029
Brock, Bradley W.; Granville, Andrew
2001
Upper bounds for $$|L(1,\chi)|$$. Zbl 1022.11041
Granville, Andrew; Soundararajan, K.
2002
When the sieve works. Zbl 1326.11055
Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa
2015
On pairs of coprime integers with no large prime factors. Zbl 0745.11043
Granville, Andrew
1991
Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032
Granville, Andrew; Soundararajan, Kannan
2008
An uncertainty principle for arithmetic sequences. Zbl 1139.11040
Granville, Andrew; Soundararajan, K.
2007
Integers, without large prime factors, in arithmetic progressions. II. Zbl 0792.11036
Granville, Andrew
1993
On complementary decompositions of the complete graph. Zbl 0674.05050
Granville, Andrew; Moisiadis, Alexandros; Rees, Rolf
1989
On the size of the first factor of the class number of a cyclotomic field. Zbl 0701.11051
Granville, A.
1990
On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034
Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C.
1990
Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129
Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej
2008
Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028
Granville, Andrew
2007
Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039
Fung, Gilbert; Granville, Andrew; Williams, Hugh C.
1992
It is easy to determine whether a given integer is prime. Zbl 1110.11002
Granville, Andrew
2005
Estimates for representation numbers of quadratic forms. Zbl 1135.11020
Blomer, Valentin; Granville, Andrew
2006
Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001
Granville, Andrew
2006
On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005
Cai, Tianxin; Granville, Andrew
2002
Big biases amongst products of two primes. Zbl 1347.11067
Dummit, David; Granville, Andrew; Kisilevsky, Hershy
2016
Smooth-supported multiplicative functions in arithmetic progressions beyond the $$x^{1/2}$$-barrier. Zbl 1428.11174
Drappeau, Sary; Granville, Andrew; Shao, Xuancheng
2017
Sum-product formulae. Zbl 1407.11043
Granville, Andrew; Solymosi, József
2016
The prime factors of Wendt’s binomial circulant determinant. Zbl 0767.11059
Fee, Greg; Granville, Andrew
1991
On a paper of Agur, Fraenkel and Klein. Zbl 0755.05005
Granville, Andrew
1991
The number of sumsets in a finite field. Zbl 1223.11028
Alon, Noga; Granville, Andrew; Ubis, Adrián
2010
Different approaches to the distribution of primes. Zbl 1275.11129
Granville, Andrew
2010
Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123
Granville, Andrew
2007
Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109
Granville, Andrew; Kurlberg, Pär
2008
On sharp transitions in making squares. Zbl 1321.11122
Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad
2012
A binary additive problem of Erdős and the order of $$2 \bmod {p^2}$$. Zbl 0912.11003
Granville, Andrew; Soundararajan, K.
1998
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.
2003
On the least prime in certain arithmetic progression. Zbl 0658.10049
Granville, Andrew; Pomerance, Carl
1990
Checking the Goldbach conjecture on a vector computer. Zbl 0679.10002
Granville, A.; Van de Lune, J.; te Riele, H. J. J.
1989
Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011
Balog, Antal; Granville, Andrew; Solymosi, Jozsef
2017
Limitations to the equi-distribution of primes. IV. Zbl 0736.11049
Friedlander, John; Granville, Andrew
1991
Visibility in the plane. Zbl 1176.11027
Adhikari, Sukumar Das; Granville, Andrew
2009
Zeta functions for ideal classes in real quadratic fields, at $$s=0$$. Zbl 1276.11180
Biró, András; Granville, Andrew
2012
Uniform distribution. Zbl 1142.11054
Granville, Andrew; Rudnick, Zeév
2007
Powerful numbers and Fermat’s Last Theorem. Zbl 0595.10011
Granville, Andrew
1986
Aurifeuillian factorization. Zbl 1107.11050
Granville, Andrew; Pleasants, Peter
2006
An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092
Granville, Andrew; Mollin, R. A.; Williams, H. C.
2000
On a problem of Hering concerning orthogonal covers of $${\mathbf K}_ n$$. Zbl 0839.05025
Granville, A.; Gronau, H.-D. O. F.; Mullin, R. C.
1995
Smoothing ‘smooth’ numbers. Zbl 0795.11041
Friedlander, John B.; Granville, Andrew
1993
Friable density. (Densité des friables.) Zbl 1318.11121
de la Bretèche, Régis; Granville, Andrew
2014
Ranks of quadratic twists of elliptic curves. Zbl 1365.11070
Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F.
2014
The frequency and the structure of large character sums. Zbl 1409.11079
Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris
2018
A more intuitive proof of a sharp version of Halász’s theorem. Zbl 1456.11182
Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan
2018
Large character sums: Burgess’s theorem and zeros of $$L$$-functions. Zbl 1444.11177
Granville, Andrew; Soundararajan, Kannan
2018
Close lattice points on circles. Zbl 1229.11124
Cilleruelo, Javier; Granville, Andrew
2009
Negative values of truncations to $$L(1,\chi)$$. Zbl 1214.11093
Granville, Andrew; Soundararajan, K.
2007
Prime divisors are Poisson distributed. Zbl 1118.11005
Granville, Andrew
2007
The least common multiple and lattice points on hyperbolas. Zbl 0983.11058
Granville, Andrew; Jiménez-Urroz, Jorge
2000
Rabinowitsch revisited. Zbl 0985.11040
Granville, Andrew; Mollin, Richard A.
2000
The set of differences of a given set. Zbl 0983.05077
Granville, Andrew; Roesler, Friedrich
1999
On positive integers $$\leq x$$ with prime factors $$\leq t\,\log \,x$$. Zbl 0686.10031
Granville, Andrew
1989
Bounding the coefficients of a divisor of a given polynomial. Zbl 0713.12001
Granville, Andrew
1990
Representing binomial coefficients as sums of squares. Zbl 0717.11016
Granville, Andrew; Zhu, Yiliang
1990
When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105
Granville, Andrew; Shao, Xuancheng
2018
Bombieri-Vinogradov for multiplicative functions, and beyond the $$x^{1/2}$$-barrier. Zbl 07066543
Granville, Andrew; Shao, Xuancheng
2019
The Frobenius postage stamp problem, and beyond. Zbl 07301143
Granville, A.; Shakan, G.
2020
Bombieri-Vinogradov for multiplicative functions, and beyond the $$x^{1/2}$$-barrier. Zbl 07066543
Granville, Andrew; Shao, Xuancheng
2019
A new proof of Halász’s theorem, and its consequences. Zbl 1443.11200
Granville, Andrew; Harper, Adam J.; Soundararajan, K.
2019
Prime suspects. The anatomy of integers and permutations. Illustrated by Robert J. Lewis. Zbl 1423.00004
Granville, Andrew; Granville, Jennifer
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
2019
Number theory revealed: an introduction. Zbl 1454.11001
Granville, Andrew
2019
The frequency and the structure of large character sums. Zbl 1409.11079
Bober, Jonathan; Goldmakher, Leo; Granville, Andrew; Koukoulopoulos, Dimitris
2018
A more intuitive proof of a sharp version of Halász’s theorem. Zbl 1456.11182
Granville, Andrew; Harper, Adam J.; Soundararajan, Kannan
2018
Large character sums: Burgess’s theorem and zeros of $$L$$-functions. Zbl 1444.11177
Granville, Andrew; Soundararajan, Kannan
2018
When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105
Granville, Andrew; Shao, Xuancheng
2018
Planck-scale mass equidistribution of toral Laplace eigenfunctions. Zbl 1376.58012
Granville, Andrew; Wigman, Igor
2017
Smooth-supported multiplicative functions in arithmetic progressions beyond the $$x^{1/2}$$-barrier. Zbl 1428.11174
Drappeau, Sary; Granville, Andrew; Shao, Xuancheng
2017
Gaps between fractional parts, and additive combinatorics. Zbl 1430.11011
Balog, Antal; Granville, Andrew; Solymosi, Jozsef
2017
Squares in arithmetic progressions and infinitely many primes. Zbl 1391.11115
Granville, Andrew
2017
Big biases amongst products of two primes. Zbl 1347.11067
Dummit, David; Granville, Andrew; Kisilevsky, Hershy
2016
Sum-product formulae. Zbl 1407.11043
Granville, Andrew; Solymosi, József
2016
Primes in intervals of bounded length. Zbl 1319.11064
Granville, Andrew
2015
When the sieve works. Zbl 1326.11055
Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa
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
2015
About the cover: a new mathematical celebrity. Zbl 1310.01017
Granville, Andrew
2015
Friable density. (Densité des friables.) Zbl 1318.11121
de la Bretèche, Régis; Granville, Andrew
2014
Ranks of quadratic twists of elliptic curves. Zbl 1365.11070
Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F.
2014
Multiplicative functions in arithmetic progressions. Zbl 1306.11078
Balog, Antal; Granville, Andrew; Soundararajan, Kannan
2013
On sharp transitions in making squares. Zbl 1321.11122
Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad
2012
Zeta functions for ideal classes in real quadratic fields, at $$s=0$$. Zbl 1276.11180
Biró, András; Granville, Andrew
2012
The distribution of the zeros of random trigonometric polynomials. Zbl 1218.60042
Granville, Andrew; Wigman, Igor
2011
Prime factors of dynamical sequences. Zbl 1290.11019
Faber, Xander; Granville, Andrew
2011
The number of sumsets in a finite field. Zbl 1223.11028
Alon, Noga; Granville, Andrew; Ubis, Adrián
2010
Different approaches to the distribution of primes. Zbl 1275.11129
Granville, Andrew
2010
Visibility in the plane. Zbl 1176.11027
Adhikari, Sukumar Das; Granville, Andrew
2009
Close lattice points on circles. Zbl 1229.11124
Cilleruelo, Javier; Granville, Andrew
2009
Pretentiousness in analytic number theory. Zbl 1236.11086
Granville, Andrew
2009
Smooth numbers: computational number theory and beyond. Zbl 1230.11157
Granville, Andrew
2008
Pretentious multiplicative functions and an inequality for the zeta-function. Zbl 1187.11032
Granville, Andrew; Soundararajan, Kannan
2008
Irreducibility and greatest common divisor algorithms for sparse polynomials. Zbl 1270.11129
Filaseta, Michael; Granville, Andrew; Schinzel, Andrzej
2008
Poisson statistics via the Chinese remainder theorem. Zbl 1211.11109
Granville, Andrew; Kurlberg, Pär
2008
Corrigendum to “Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis”. Zbl 1235.11092
Granville, Andrew
2008
Running time predictions for factoring algorithms. Zbl 1205.11132
Croot, Ernie; Granville, Andrew; Pemantle, Robin; Tetali, Prasad
2008
Prime number patterns. Zbl 1145.11069
Granville, Andrew
2008
Large character sums: pretentious characters and the Pólya-Vinogradov theorem. Zbl 1210.11090
Granville, Andrew; Soundararajan, K.
2007
Sieving and the Erdős-Kac theorem. Zbl 1145.11071
Granville, Andrew; Soundararajan, K.
2007
Lattice points on circles, squares in arithmetic progressions and sumsets of squares. Zbl 1183.11058
Cilleruelo, Javier; Granville, Andrew
2007
An uncertainty principle for arithmetic sequences. Zbl 1139.11040
Granville, Andrew; Soundararajan, K.
2007
Rational and integral points on quadratic twists of a given hyperelliptic curve. Zbl 1129.11028
Granville, Andrew
2007
Refinements of Goldbach’s conjecture, and the generalized Riemann hypothesis. Zbl 1230.11123
Granville, Andrew
2007
Uniform distribution. Zbl 1142.11054
Granville, Andrew; Rudnick, Zeév
2007
Negative values of truncations to $$L(1,\chi)$$. Zbl 1214.11093
Granville, Andrew; Soundararajan, K.
2007
Prime divisors are Poisson distributed. Zbl 1118.11005
Granville, Andrew
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
Granville, Andrew; Rudnick, Zeév
2007
An introduction to additive combinatorics. Zbl 1183.11007
Granville, Andrew
2007
The distribution of roots of a polynomial. Zbl 1170.11016
Granville, Andrew
2007
Torsion points on curves. Zbl 1172.11020
Granville, Andrew; Rudnick, Zeév
2007
Prime number races. Zbl 1139.11037
Granville, Andrew; Martin, Greg
2006
Extreme values of $$|\zeta(1+it)|$$. Zbl 1131.11055
Granville, Andrew; Soundararajan, K.
2006
Estimates for representation numbers of quadratic forms. Zbl 1135.11020
Blomer, Valentin; Granville, Andrew
2006
Cycle lengths in a permutation are typically Poisson. Zbl 1171.05001
Granville, Andrew
2006
Aurifeuillian factorization. Zbl 1107.11050
Granville, Andrew; Pleasants, Peter
2006
Residue races. Zbl 1161.11300
Granville, Andrew; Shiu, Daniel; Shiu, Peter
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
2005
It is easy to determine whether a given integer is prime. Zbl 1110.11002
Granville, Andrew
2005
Prime number races. Zbl 1358.11139
Granville, Andrew; Martin, Greg
2005
The square of the Fermat quotient. Zbl 1083.11005
Granville, Andrew
2004
Errata to: The distribution of values of $$L(1,\chi_d)$$. Zbl 1188.11039
Granville, A.; Soundararajan, K.
2004
The distribution of values of $$L(1,\chi_d)$$. Zbl 1044.11080
Granville, Andrew; Soundararajan, K.
2003
Decay of mean values of multiplicative functions. Zbl 1047.11093
Granville, Andrew; Soundararajan, K.
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.
2003
It’s as easy as $$abc$$. Zbl 1160.11318
Granville, Andrew; Tucker, Thomas J.
2002
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
2002
Upper bounds for $$|L(1,\chi)|$$. Zbl 1022.11041
Granville, Andrew; Soundararajan, K.
2002
On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005
Cai, Tianxin; Granville, Andrew
2002
Unit fractions and the class number of a cyclotomic field. Zbl 1056.11059
Croot, Ernest S. III; Granville, Andrew
2002
Large character sums. Zbl 0983.11053
Granville, Andrew; Soundararajan, K.
2001
The spectrum of multiplicative functions. Zbl 1036.11042
Granville, Andrew; Soundararajan, K.
2001
More points than expected on curves over finite field extensions. Zbl 1023.11029
Brock, Bradley W.; Granville, Andrew
2001
Zeros of Fekete polynomials. Zbl 1007.11053
Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K.
2000
$$ABC$$ implies no “Siegel zeros” for $$L$$-functions of characters with negative discriminant. Zbl 0967.11033
Granville, Andrew; Stark, H. M.
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.
2000
The least common multiple and lattice points on hyperbolas. Zbl 0983.11058
Granville, Andrew; Jiménez-Urroz, Jorge
2000
Rabinowitsch revisited. Zbl 0985.11040
Granville, Andrew; Mollin, Richard A.
2000
Borwein and Bradley’s Apéry-like formulae for $$\zeta(4n+3)$$. Zbl 0976.11035
Almkvist, Gert; Granville, Andrew
1999
The set of differences of a given set. Zbl 0983.05077
Granville, Andrew; Roesler, Friedrich
1999
On the scarcity of powerful binomial coefficients. Zbl 1033.11007
Granville, Andrew
1999
Motivating the multiplicative spectrum. Zbl 0935.11033
Granville, Andrew; Soundararajan, K.
1999
$$abc$$ allows us to count squarefrees. Zbl 0924.11018
Granville, Andrew
1998
On the exponential sum over $$k$$-free numbers. Zbl 0922.11071
Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D.
1998
A binary additive problem of Erdős and the order of $$2 \bmod {p^2}$$. Zbl 0912.11003
Granville, Andrew; Soundararajan, K.
1998
Arithmetic properties of binomial coefficients. I: Binomial coefficients modulo prime powers. Zbl 0903.11005
Granville, Andrew
1997
A decomposition of Riemann’s zeta-function. Zbl 0907.11024
Granville, Andrew
1997
Correction to: Zaphod Beeblebrox’s brain and the fifty-ninth row of Pascal’s triangle. Zbl 0889.05004
Granville, Andrew
1997
Defect zero $$p$$-blocks for finite simple groups. Zbl 0855.20007
Granville, Andrew; Ono, Ken
1996
Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Zbl 0868.11009
Granville, Andrew; Ramaré, Olivier
1996
Values of Bernoulli polynomials. Zbl 0856.11008
Granville, Andrew; Sun, Zhi-Wei
1996
On the equations $$z^ m = F(x,y)$$ and $$Ax^ p + By^ q = Cz^ r$$. Zbl 0838.11023
Darmon, Henri; Granville, Andrew
1995
Harald Cramér and the distribution of prime numbers. Zbl 0833.01018
Granville, Andrew
1995
Unexpected irregularities in the distribution of prime numbers. Zbl 0843.11043
Granville, Andrew
1995
On a problem of Hering concerning orthogonal covers of $${\mathbf K}_ n$$. Zbl 0839.05025
Granville, A.; Gronau, H.-D. O. F.; Mullin, R. C.
1995
On the number of solution of the equation $$\sum_{i=1}^ n x_ i/d_ i \equiv 0 \pmod 1$$, and of diagonal equations in finite fields. Zbl 0837.11017
Granville, Andrew; Li, Shuguang; Sun, Qi
1995
On the number of solutions to the generalized Fermat equation. Zbl 0836.11014
Granville, Andrew
1995
There are infinitely many Carmichael numbers. Zbl 0816.11005
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
On the difficulty of finding reliable witnesses. Zbl 0828.11074
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
...and 38 more Documents
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#### Cited by 1,266 Authors

 44 Shparlinski, Igor E. 33 Granville, Andrew James 24 Luca, Florian 21 Soundararajan, Kannan 18 Banks, William D. 15 Lamzouri, Youness 14 Sun, Zhi-Wei 13 Pomerance, Carl Bernard 12 Ford, Kevin B. 12 Matomäki, Kaisa Sofia 11 Pollack, Paul 10 Harper, Adam J. 10 Radziwiłł, Maksym 9 Moree, Pieter 9 Ramaré, Olivier 8 Bennett, Michael A. 8 Meštrović, Romeo 8 Pan, Hao 8 Tao, Terence 8 Tenenbaum, Gérald 8 Zhang, Zhenxiang 7 Bradley, David M. 7 Cilleruelo, Javier 7 Konyagin, Sergeĭ Vladimirovich 7 Maynard, James 7 Shao, Xuancheng 7 Zaharescu, Alexandru 6 Bourgain, Jean 6 Drappeau, Sary 6 Elsholtz, Christian 6 Erdélyi, Tamás 6 Freiberg, Tristan 6 Friedlander, John Benjamin 6 Ji, Lijun 6 Martin, Greg 6 Munsch, Marc 6 Ohno, Yasuo 6 Rudnick, Zeév 6 Stănică, Pantelimon 6 Wigman, Igor 6 Winterhof, Arne 6 Wu, Jie 5 Alkan, Emre 5 Baruah, Nayandeep Deka 5 Borwein, Peter Benjamin 5 Croot, Ernie 5 Dietmann, Rainer 5 Eie, Minking 5 Freitas, Nuno 5 Gao, Weidong 5 Goldmakher, Leo 5 Hoffman, Michael E. 5 Lau, Yuk-Kam 5 Lemke Oliver, Robert J. 5 Moshe, Yossi 5 Ostafe, Alina 5 Poonen, Bjorn 5 Silverman, Joseph Hillel 5 Tauraso, Roberto 5 Tucker, Thomas John 4 Aistleitner, Christoph 4 Bhowmik, Gautami 4 Cai, Tianxin 4 Chen, Imin 4 Chen, Yonggao 4 Chu, Wenchang 4 David, Chantal 4 Dieulefait, Luis Victor 4 González-Jiménez, Enrique 4 Grantham, Jon 4 Green, Ben Joseph 4 Hajdu, Lajos 4 Hildebrand, Adolf J. 4 Kerr, Bryce 4 Koukoulopoulos, Dimitris 4 Kowalski, Emmanuel 4 Lagarias, Jeffrey C. 4 Meidl, Wilfried 4 Montgomery, Hugh Lowell 4 Pacifici, Emanuele 4 Poly, Guillaume 4 Stinson, Douglas Robert 4 Stoll, Michael 4 Sun, Zhihong 4 Tong-Viet, Hung P. 4 Voloch, José Felipe 4 Wang, Yingnan 4 Yazdani, Soroosh 3 Akbary, Amir 3 Amoroso, Francesco 3 Balog, Antal 3 Bank, Efrat 3 Bary-Soroker, Lior 3 Berkovich, Alexander 3 Billerey, Nicolas 3 Bober, Jonathan W. 3 Borwein, Jonathan Michael 3 Bridy, Andrew 3 Brough, Julian M. A. 3 Bucur, Alina ...and 1,166 more Authors
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#### Cited in 229 Serials

 159 Journal of Number Theory 62 International Journal of Number Theory 58 Mathematics of Computation 37 Proceedings of the American Mathematical Society 30 Discrete Mathematics 29 Transactions of the American Mathematical Society 26 Journal of Algebra 26 The Ramanujan Journal 23 Mathematika 22 Journal de Théorie des Nombres de Bordeaux 21 Mathematical Proceedings of the Cambridge Philosophical Society 17 Acta Arithmetica 16 Functiones et Approximatio. Commentarii Mathematici 16 Mathematische Annalen 16 Monatshefte für Mathematik 15 Bulletin of the Australian Mathematical Society 15 Advances in Mathematics 15 Archiv der Mathematik 14 Compositio Mathematica 14 Bulletin of the American Mathematical Society. New Series 13 Journal of Combinatorial Theory. Series A 13 Experimental Mathematics 13 Finite Fields and their Applications 12 Integers 11 Designs, Codes and Cryptography 10 Journal d’Analyse Mathématique 10 Annals of Mathematics. Second Series 9 Israel Journal of Mathematics 9 Journal of Mathematical Analysis and Applications 9 Rocky Mountain Journal of Mathematics 8 American Mathematical Monthly 8 Communications in Algebra 8 Duke Mathematical Journal 8 Journal of the Australian Mathematical Society 8 Science China. Mathematics 7 Mathematical Notes 7 Czechoslovak Mathematical Journal 7 Mathematische Zeitschrift 7 Michigan Mathematical Journal 7 Journal of the European Mathematical Society (JEMS) 7 Acta Mathematica Sinica. English Series 6 Journal für die Reine und Angewandte Mathematik 6 Revista Matemática Iberoamericana 6 Journal of the American Mathematical Society 6 Geometric and Functional Analysis. GAFA 6 Indagationes Mathematicae. New Series 6 Algebra & Number Theory 5 Discrete Applied Mathematics 5 Annales de l’Institut Fourier 5 Journal of Complexity 5 Journal of Combinatorial Designs 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Bulletin of the London Mathematical Society 4 Journal of Pure and Applied Algebra 4 Nagoya Mathematical Journal 4 Pacific Journal of Mathematics 4 Theoretical Computer Science 4 European Journal of Combinatorics 4 Journal of Symbolic Computation 4 Elemente der Mathematik 4 Journal of Group Theory 4 Annals of Combinatorics 4 Journal of Integer Sequences 4 Mediterranean Journal of Mathematics 4 Forum of Mathematics, Sigma 4 Research in Number Theory 3 Communications in Mathematical Physics 3 The Mathematical Intelligencer 3 Canadian Journal of Mathematics 3 Canadian Mathematical Bulletin 3 Inventiones Mathematicae 3 Journal of Functional Analysis 3 Journal of the Mathematical Society of Japan 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Acta Mathematica Hungarica 3 Graphs and Combinatorics 3 Probability Theory and Related Fields 3 Journal of Cryptology 3 International Journal of Foundations of Computer Science 3 Aequationes Mathematicae 3 Stochastic Processes and their Applications 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Expositiones Mathematicae 3 Advances in Applied Clifford Algebras 3 Journal of Inequalities and Applications 3 Journal of Statistical Mechanics: Theory and Experiment 3 Japanese Journal of Mathematics. 3rd Series 3 Research in the Mathematical Sciences 2 Information Processing Letters 2 Journal of Mathematical Physics 2 The Mathematical Gazette 2 Mathematische Semesterberichte 2 Nonlinearity 2 Theory of Probability and its Applications 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Illinois Journal of Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Manuscripta Mathematica 2 Proceedings of the London Mathematical Society. Third Series ...and 129 more Serials
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#### Cited in 49 Fields

 1,018 Number theory (11-XX) 173 Combinatorics (05-XX) 79 Algebraic geometry (14-XX) 72 Group theory and generalizations (20-XX) 46 Probability theory and stochastic processes (60-XX) 40 Dynamical systems and ergodic theory (37-XX) 36 Information and communication theory, circuits (94-XX) 32 Computer science (68-XX) 26 Special functions (33-XX) 25 Field theory and polynomials (12-XX) 24 Functions of a complex variable (30-XX) 18 Commutative algebra (13-XX) 17 Global analysis, analysis on manifolds (58-XX) 11 Associative rings and algebras (16-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Numerical analysis (65-XX) 10 Partial differential equations (35-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Ordinary differential equations (34-XX) 8 Convex and discrete geometry (52-XX) 7 Real functions (26-XX) 7 Sequences, series, summability (40-XX) 6 History and biography (01-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Mathematical logic and foundations (03-XX) 5 Measure and integration (28-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Differential geometry (53-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Nonassociative rings and algebras (17-XX) 4 Geometry (51-XX) 4 Quantum theory (81-XX) 3 Potential theory (31-XX) 3 Approximations and expansions (41-XX) 3 Manifolds and cell complexes (57-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 Algebraic topology (55-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-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 Statistics (62-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)

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