Publications by year:
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Preprints
Andrew Granville
's
complete research publications
By subject:
Analytic
,
Algebraic
,
Algorithmic
, and
Combinatorial
number theory,
other research
, and
expository writing.
(Papers listed in reverse chronological order)
PreP:
Poisson statistics via the Chinese Remainder Theorem
(with Par Kurlberg)
PreP:
The number of possibilities for random dating
(with Aaron Abrams and Rod Canfield)
PreP:
Sharp transitions in making squares
(with Ernest S. Croot III and Prasad Tetali)
PreP:
Zeta functions for ideal classes in real quadratic fields, at s=0
(with Andras Biro)
PreP:
Close lattice points on circles
(with Javier Cilleruelo)
PreP:
Multiplicative functions in arithmetic progressions
(with Antal Balog and K. Soundararajan)
Accp:
Irreducibility and Greatest Common Divisor Algorithms for Sparse Polynomials
(with Mike Filaseta and Andrzej Schinzel)
Number Theory and Polynomials, Heilbronn Institute Proceedings
Accp:
Prime number patterns
American Mathematical Monthly
Accp:
Pretentious multiplicative functions and an inequality for the zeta-function
(
with K. Soundararajan)
Proceedings, Anatomy of Integers workshop, Montreal 2006
Accp:
Lattice points on circles, squares in arithmetic progressions, and sumsets of squares
(with Javier Cilleruelo)
Proceedings, Additive Combinatorics workshop, Montreal 2006
Accp:
Negative values of truncations to L(1,chi)
(
with K. Soundararajan)
Proceedings, Gauss-Dirichlet workshop, Gottingen 2006
Accp:
Refinements of Goldbach's conjecture, and the Generalized Riemann Hypothesis
Functiones et Approximatio (Deshouillers volume)
2007:
Rational and integral points on quadratic twists of a given hyperelliptic curve
International Mathematical Research Notices
2007:
Large character sums: Pretentious characters and the Polya-Vinogradov theorem
(
with K.Soundararajan)
Journal of the American Mathematical Society
2007:
An uncertainty principle for arithmetic sequences
(
with K. Soundararajan)
Annals of Mathematics
2007:
Sieving and the Erdos-Kac theorem
(with K. Soundararajan)
Proceedings, NATO-SMS ASI, Montreal 2005
2007:
Prime divisors are Poisson distributed
International Journal of Number Theory
2007:
Extreme values of |zeta(1+it)|
(with K. Soundararajan)
Proceedings,
Bangalore
Conference, 2003
2006:
Estimates for the representation numbers of binary quadratic forms
(with Valentin Blomer)
Duke Mathematical Journal
2006:
Cycle lengths in a permutation are typically Poisson distributed
Electronic Journal of Combinatorics
2006:
Aurefeuillian factorization revisited
(with Peter Pleasants)
Mathematics of Computation
2006:
Residue races
( with Peter and Daniel Shiu)
Ramanujan Journal
2006:
Prime number races
(with Greg Martin)
American Mathematical Monthly
2005:
On the Distribution of Rational Functions Along a Curve over F_p and Residue Races
(with Igor Shparlinski and Alexandru Zaharescu)
Journal of Number Theory
2005:
It is easy to determine whether a given integer is prime
Bulletin of the American Mathematical Society
2004:
The square of the Fermat quotient
Electronic journal of combinatorial number theory
2004:
The number of unsieved integers up to x
(with K. Soundararajan)
Acta Arithmetica
2003:
The number of fields generated by the square root of values of a given polynomial
(with Pam Cutter and Tom Tucker)
Canadian Mathematical Bulletin
2003:
Decay of mean-values of multiplicative functions
(with K. Soundararajan)
Canadian Journal of Mathematics
2003:
Distribution of values of L(1,chi
d
)
(with K. Soundararajan)
Geometric and Functional Analysis
2002:
Two contradictory conjectures concerning Carmichael numbers
, (with Carl Pomerance)
Mathematics of Computation
2002:
Upper bounds for |L(1,chi)|
,(with K. Soundararajan)
Quarterly Journal of Mathematics
2002:
Unit fractions and the class number of a cyclotomic field
, (with Ernest S. Croot III)
Journal of the London Mathematical Society
2001:
More points on curves over finite field extensions than expected
(with Brad Brock)
Finite Fields and their Applications
2001:
Product of integers in an interval, modulo squares
(with John Selfridge)
Electronic Journal of Combinatorics
2001:
Large Character Sums
(with K. Soundararajan)
Journal of the American Mathematical Society
2001:
The spectrum of multiplicative functions
(with K. Soundararajan)
Annals of Mathematics
2001:
Rabinowitsch revisited
(with Richard Mollin)
Acta Arithmetica
2000:
ABC implies no "Siegel Zeroes'' for L-functions of characters with negative discriminant
(with Harold M. Stark )
Inventiones Mathematicae
2000:
An upper bound on the least inert prime in a real quadratic field
(with Richard Mollin and Hugh C. Williams)
Canadian Journal of Mathematics
2000:
Zeros of Fekete polynomials
(with Brian Conrey, K. Soundararajan, and Bjorn Poonen)
Annales de l'Institut Fourier
2000:
The least common multiple and lattice points on hyperbolas
(with Jorge Jiménez-Urroz )
Quarterly Journal of Mathematics
1999:
Motivating the multiplicative spectrum
(with K. Soundararajan)
Proc, Urbana Conference
1999:
The set of differences of a given set
(with F. Roesler)
American Mathematical Monthly
1999:
Borwein and Bradley's Apéry-like formulae for
zeta(4n+3)
(with Gert Almkvist)
Experimental Mathematics
1999:
On the scarcity of powerful binomial coefficients
Mathematika
1998:
On the exponential sum over k-free numbers
(with Joerg Brudern, Alberto Perelli, Bob Vaughan and Trevor Wooley)
Philosophical Transactions of the Royal Society
1998:
A binary additive problem of
Erdös
and the order of
2 mod p
2
(with K. Soundararajan)
Ramanujan Journal
1998:
ABC allows us to can count squarefrees
International Mathematical Research Notices
1997:
A Decomposition of Riemann's Zeta-Function
London Mathematical Society Lecture Notes
1997:
Primes at a (somewhat lenghty) glance
(with Takashi Agoh and Paul Erdos)
American Mathematical Monthly
1997:
Arithmetic Properties of Binomial Coefficients I: Binomial coefficients modulo prime powers
CMS Conf Proc
1996:
Special Values of Bernoulli polynomials
(with Zhi-Wei Sun)
Pacific Journal of Mathematics
1996:
Defect zero p-blocks for finite simple groups
(with Ken Ono)
Transactions of the American Mathematical Society
1996:
Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients
(with Olivier Ramaré )
Mathematika
1995:
On the number of co-prime-free sets
(with Neil J. Calkin)
New Yòrk Seminar
1995:
On the number of solutions to the equation a_1/x_1 + ... + a_n/x_n = 0 mod 1
(with Shuguang Li and Sun Qi)
Sichuan Daxue Xuebao
1995:
The number of fugitive primes,
(appendix to "Rational torsion of prime order in elliptic curves over number fields",
a paper by Sheldon Kamienny and Barry Mazur)
Astérisque
1995:
Harold Cramér and the distribution of prime numbers
Scandanavian Actuarial J.
1995:
On the equations z
m
=F(x,y) and Ax
p
+By
q
=Cz
r
(with Henri Darmon)
Bulletin on the London Mathematical Society,
1995:
On a problem of Hering concerning orthogonal covers of
K
n
(with H.-D. Gronau and R.C. Mullin)
JCT A
1995:
On the number of solutions to the generalized Fermat equation
Proceedings, CNTA IV
1995:
Unexpected irregularities in the distribution of prime numbers
Proceedings. ICM
1994:
There are infinitely many Carmichael numbers
(with Red Alford and Carl Pomerance)
Annals of Mathematics
1994:
On sparse languages L such that LL=\SUM*
(with Per Enflo, Jeffrey Shallit and Sheng Yu)
Discrete Mathematics
1994:
On the difficulty of finding reliable witnesses
(with Red Alford and Carl Pomerance)
ANTS-I
1993:
The Kummer-Wieferich-Skula criteria for the first case of Fermat's Last Theorem
Proceedings,
CNTA III
1993:
On integers, without large prime factors, in arithmetic progressions I
Acta Mathematica
1993:
An upper bound in Goldbach's problem
(with Jean-Marc Deshouillers, Wladyslawz and Carl Pomerance)
Mathematics of Computation
1993:
Solution to a problem of Bombieri
Atti della Accademia Nazionale dei Lincei
1993:
Smoothing "smooth" numbers
(with John B. Friedlander)
Philosophical Transactions of the Royal Society
1993:
On integers, without large prime factors, in arithmetic progressions II
Philosophical Transactions of the Royal Society
1992:
Limitations to the equi-distribution of primes III
Compositio Mathematicae
1992:
Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle
American Mathematical Monthly
1992:
Finding integers k for which a given Diophantine Equation has no solution in kth powers of integers
Acta Arithmetica
1992:
Squares in arithmetic progressions
(with Enrico Bombieri and Janos Pintz)
Duke Mathematical Journal,
1992:
Computation on the first factor of the class number of cyclotomic fields
(with Gilbert Fung and Hugh C. Williams)
Journal of Number Theory
1992:
On elementary proofs of the Prime Number Theorem for arithmetic progressions, without characters
Proceedings, Amalfi Conference
1992:
Relevance of the residue class to the abundance of primes
(with John B. Friedlander)
Proceedings, Amalfi Conference
1991:
Subdesigns in Steiner Quadruple Systems
(with Alan Hartman)
Journal of Combinatorial Theory
1991:
A note on sums of primes
Canadian Mathematical Bulletin
1991:
Oscillation theorems for primes in arithmetic progressions and for sifting functions
(with John B. Friedlander, Adolf Hildebrand and Helmut Maier)
Journal of the American Mathematical Society
1991:
The lattice points of an n-dimensional tetrahedron
Aequationes Mathematicae
1991:
The prime factors of Wendt's binomial circulant determinant
(with Greg J. Fee)
Mathematics of Computation
1991:
Limitations to the equi-distribution of primes, IV
(with John B. Friedlander)
Proceedings of the Royal Society
1991:
On a paper of Agur, Fraenkel and Klein
Discrete Mathematics
1991:
On pairs of coprime integers with no large prime factors
Expositiones Mathematicae
1990:
Some conjectures related to Fermat's Last Theorem
Proc CNTA1, Banff
1990:
Defining Bernoulli polynomials in Z/pZ (A generic regularity condition)
(with Herb S. Shank)
Proc AMS
1990:
Representing binomial coefficients as sums of squares
(with Yiliang Zhu)
American Mathematical Monthly
1990:
On the size of the first factor of the class number of a cyclotomic field
Inventiones Mathematicae
1990:
Some conjectures in Analytic Number Theory and their connection with Fermat's Last Theorem
Proc. Urbana conference
1990:
On the normal behavior of the iterates of some arithmetic functions
(with Paul Erdos, Carl Pomerance and Claudia Spiro)
Proceedings Urbana conference
1990:
Bounding the coefficients of a divisor of a given polynomial
Monatshefte fur Mathematik,
1990:
On the least prime in certain arithmetic progressions
(with Carl Pomerance)
Journal of the London Mathematical Society
1989:
On complementary decompositions of the complete graph
(with Alexandros Moisiadis and Rolf Rees)
Graphs and Combinatorics
1989:
On a class of determinants
Fibonacci Quarterly
1989:
On positive integers <=x with prime factors <= t log x.
NATO ASI, Banff
1989:
Checking the Goldbach Conjecture on a vector computer
(with J. Van de Lune and Herman te Riele)
NATO ASI, Banff
1989:
Limitations to the equi-distribution of primes I
(with John B. Friedlander)
Annals of Mathematics
1989:
Least primes in arithmetic progressions
Proc CNTA 0, Laval
1988:
The First Case of Fermat's Last Theorem is true for all prime exponents up to 714,591,416,091,389
(with Michael B. Monagan)
Transactions of the American Mathematical Society
1988:
On Sophie Germain type criteria for Fermat's Last Theorem
(with Barry J. Powell)
Acta Arithmetica
1988:
Nested Steiner n-cycle systems and perpendicular arrays
(with Alexandros Moisiadis and Rolf Rees)
Journal of Combinatorial Mathematics and Mathematical Computing
1988:
Bipartite planes
(with Alexandros Moisiadis and Rolf Rees)
Congressus Numerantium
1987:
Sophie Germain's Theorem for prime pairs p, 6p+1
Journal of Number Theory
1987:
Matrices as the sum of four squares
Linear and Multilinear Algebra
1987:
On Hajos' Conjecture (minimum cycle-partitions of the edge-set of Eulerian graphs)
(with Alexandros Moisiadis)
Congressus Numerantium
1986:
Powerful numbers and Fermat's Last Theorem
Comptes Rendus de l'Académie des Sciences du Canada
1986:
On Krasner's criteria for the first case of Fermat's Last Theorem
Manuscripta Mathematica
1985:
Refining the conditions on the Fermat quotient
Mathematical Proceedings of the Cambridge Philosophical Society
1985:
The set of exponents, for which Fermat's Last Theorem is true, has density one
Comptes Rendus de l'Académie des Sciences du Canada
Updated
:
November 1, 2006