Andrew Granville: Articles, reprints and preprints
This page gives access to most of my reprints and preprints.
I have sorted the papers by subject area on this page, though
here is an (unlinked)
list of publications .
Below is a list of general subject areas. Clicking on the most appropriate
subject area will take you to my papers in that area. Clicking on the
name of a paper will give you a postscript version of the paper.
The TeX file is sometimes available.
(Warning: There may be some copyright problems
if you use any published paper for anything other than your own
scholarly use, so beware.)
Last updated: November 2000.
Subject Areas
Survey Articles
Research Papers
- Andrew Granville and Carl Pomerance
Two contradictory conjectures concerning Carmichael numbers
Mathematics of Computation (to appear).
-
W. `Red' Alford, Andrew Granville and Carl Pomerance,
There are infinitely many Carmichael numbers,
Annals of Mathematics, 140 (1994), 703-722.
-
W. `Red' Alford, Andrew Granville and Carl Pomerance,
On the difficulty of finding reliable witnesses,,
Lecture Notes in Comp. Sci. 877 (1995), 1-16.
Is this subject interesting? See what
Gauss had to say
about it.
- Andrew Granville
On the scarcity of powerful binomial coefficients
Mathematika (to appear).
- Andrew Granville,
Arithmetic Properties of Binomial Coefficients (website)
Canadian Mathematical Society Conference Proceedings,
20 (1997), 253-275.
- Andrew Granville and Olivier Ramar\'e,
Explicit bounds on exponential sums, and the scarcity
of squarefree binomial coefficients.
Mathematika 43 (1996), 73-107
- Andrew Granville,
Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's
triangle
American Mathematical Monthly 99 (1992), 318-331.
Corrigendum American Mathematical Monthly 104 (1997), 848-851.
- Andrew Granville and Yiliang Zhu,
Representing binomial coefficients as sums of squares
American Mathematical Monthly 97 (1990), 486-493.
- Andrew Granville, Peter and Daniel Shiu,
Residue races
- Andrew Granville and John Selfridge
Product of integers in an interval equals a square
Electronic Journal of Combinatorics (accepted).
- Andrew Granville and Jorge Jimenez-Urroz
The least common multiple and lattice points on hyperbolas
Quart. J. Math (Oxford) 51 (2000), 343--352.
- Andrew Granville and F. Roesler
The set of differences of a given set
American Mathematical Monthly 106} (1999), 338-344.
- Gert Almkvist and Andrew Granville
Borwein and Bradley's Ap\' ery-like formulae for zeta(4n+3)
Experimental Mathematics 8 (1999), 197-204.
- Andrew Granville and K. Soundararajan
A binary additive problem of Erdos and the order of 2 mod p^2
Ramanujan Journal 2 (1998), 283-298.
- Andrew Granville
A Decomposition of Riemann's Zeta-Function
London Mathematical Society Lecture Notes 247 (1997), 95-101.
- Takashi Agoh, Paul Erdos and Andrew Granville
Primes at a (somewhat lengthy) glance
American Mathematical Monthly 104 (1997), 943-945.
- Per Enflo, Andrew Granville, Jeffrey Shallit and Sheng Yu
On weakly sparse languages L such that LL = Sigma^*
Discrete Applied Mathematics 52 (1994), 275-285.
- Enrico Bombieri, Andrew Granville and J\'anos Pintz,
Squares in arithmetic progressions
Duke Mathematical Journal 66 (1992), 369-385.
- Neil Calkin and Andrew Granville,
On the number of co-prime-free sets
Number Theory: New York Seminar 1991-1995 (eds. D. Chudnovsky,
et.al.), Springer-Verlag (1996).
- Paul Erdos, Andrew Granville,Carl Pomerance and Claudia Spiro,
On the normal behavior of the iterates of some arithmetic functions
Analytic Number Theory (ed. B.C. Berndt, H. Diamond, H. Halberstam,
A. Hildebrand), (Birkh\"auser, Boston, 1990), 165-204.
- Andrew Granville,
A note on a paper of Agur, Fraenkel and Klein
Discrete Mathematics 94 (1991), 147-151.
- Andrew Granville, H.D.O.F. Gronau and R.C. Mullin,
On a problem of Hering concerning orthogonal covers of $K_n$,
Journal of Combinatorial Theory (Series A) 72 (1995), 345-350.
- Andrew Granville and Alan Hartman,
Subdesigns in Steiner Quadruple Systems
Journal of Combinatorial Theory (Series A) 56 (1991), 239-270.
- Andrew Granville, Alexandros Moisiadis and Rolf Rees,
On complementary decompositions of the complete graph
Graphs and Combinatorics 5 (1989), 57-61.
- Andrew Granville, Alexandros Moisiadis and Rolf Rees,
Nested Steiner n-cycle systems and perpindicular arrays
Journal of Combinatorial Mathematics and Mathematical Computing
3 (1988), 163-167.
- Andrew Granville, Alexandros Moisiadis and Rolf Rees,
Bipartite planes
Congressus Numerantium 61 (1988), 241-248.
- Andrew Granville and Alexandros Moisiadis,
On Hajos' Conjecture
Congressus Numerantium 56 (1987), 183-187.
Survey Articles
Research Papers
- John B. Friedlander and Andrew Granville,
Limitations to the equi-distribution of primes I
Annals of Mathematics 129 (1989), 363-382.
- John B. Friedlander, Andrew Granville, Adolf Hildebrand and Helmut Maier
Oscillation theorems for primes in arithmetic progressions
and for sifting functions
Journal of the American Mathematical Society 4 (1991), 25-86.
- John B. Friedlander and Andrew Granville,
Limitations to the equi-distribution of primes III
Compositio Mathematicae 81 (1992), 19-32.
- John B. Friedlander and Andrew Granville,
Limitations to the equi-distribution of primes IV
Proceedings of the Royal Society (Series A) 435 (1991), 197-204.
- John B. Friedlander and Andrew Granville,
Relevance of the residue class to the abundance of primes
Proceedings of the Amalfi Conference on Analytic Number Theory,
(Salerno, Italy, 1993), 95-104.
- Brian Conrey, Andrew Granville, Bjorn Poonen and K. Soundararajan,
Zeros of Fekete polynomials.
Annales de l'Institut Fourier (Grenoble) 50 (2000), 865-889.
Research Papers
- Andrew Granville,
On the Kummer-Wieferich-Skula criteria for the first case of Fermat's
Last Theorem
in `Advances in Number Theory' (ed. F.Q. Gouvea and N. Yui),
(New York, Oxford University Press, 1993), 479-498.
- Andrew Granville and Michael B. Monagan,
The First Case of Fermat's Last Theorem is true for
all prime exponents up to 714,591,416,091,389
Transactions of the American Mathematical Society
306 (1988), 329-359.
- Andrew Granville,
The set of exponents for which Fermat's Last
Theorem is true, has density one
Comptes Rendus de l'Acad\'emie des Sciences du Canada
7 (1985), 55-60.
Early Work
- Greg J. Fee and Andrew Granville,
Computing the prime factors of Wendt's Binomial Circulant determinant
Mathematics of Computation 57 (1991), 839-848.
- Andrew Granville,
Some conjectures related to Fermat's Last Theorem
Number Theory (ed. R.A Mollin),
(de Gruyter, New York, 1990), 177-192.
- Andrew Granville,
Some conjectures in Analytic Number Theory and their
connection with Fermat's Last Theorem
Analytic Number Theory (ed. B.C. Berndt, H. Diamond, H. Halberstam,
A. Hildebrand), (Birkh\"auser, Boston, 1990), 311-326.
- Andrew Granville and Barry Powell,
On Sophie Germain type criteria for Fermat's Last Theorem
Acta Arithmetica 50 (1988), 265-277.
- Andrew Granville,
Sophie Germain's Theorem for prime pairs p, 6p+1,
Journal of Number Theory 27 (1987), 63-72.
- Andrew Granville,
Powerful numbers and Fermat's Last Theorem
Comptes Rendus de l'Acad\'emie des Sciences du Canada
8 (1986), 215-218.
- Andrew Granville,
On Krasner's criteria for the first case of Fermat's Last Theorem
Manuscripta Mathematica 56 (1986), 67-70.
- Andrew Granville,
Refining the conditions on the Fermat quotient
Mathematical Proceedings of the Cambridge
Philosophical Society 98 (1985), 5-8.
- Jean-Marc Deshouillers, Andrew Granville, Wladyslaw Narkiewicz and Carl Pomerance,
An upper bound in Goldbach's problem
Mathematics of Computation, 61 (1993), 209-213.
- Andrew Granville, J. Van de Lune and Herman te Riele,
Checking the Goldbach Conjecture on a vector computer
Number Theory and Applications (ed. R.A Mollin),
(Kluwer, NATO ASI, 1989), 423-434.
- Andrew Granville,
On integers, without large prime factors, in arithmetic progressions I,
Acta Mathematica 170 (1993), 255-273.
- Andrew Granville,
On integers, without large prime factors, in arithmetic progressions II.
Philosophical Transactions of the Royal Society, 345 (1993), 349-362.
- John B. Friedlander and Andrew Granville,
Integers without large prime factors, in short intervals
Philosophical Transactions of the Royal Society, 345 (1993), 339-348.
- Andrew Granville,
The lattice points of an n-dimensional tetrahedron
Aequationes Mathematicae 41 (1991), 234-241.
- Andrew Granville,
On pairs of coprime integers with no large prime factors
Expositiones Mathematicae 9 (1991) 335-350.
- Andrew Granville,
On positive integers <= x with prime factors <= t log x
Number Theory and Applications (ed. R.A Mollin),
(Kluwer, NATO ASI, 1989), 403-422.
- Andrew Granville,
Matrices as the sum of squares
Linear and Multilinear Algebra 20 (1987), 247-251.
- Andrew Granville,
On a class of determinants
Fibonacci Quarterly 27 (1989), 253-256.
- Andrew Granville,
Bounding the coefficients of a divisor of a given polynomial
Monatshefte f\"ur Mathematik, 109 (1990), 271-277.
- Andrew Granville,
Paulo Ribenboim on his retirement
in `Advances in Number Theory' (ed. F.Q Gouvea and N. Yui),
(New York, Oxford University Press, 1993), 469-478.
- Andrew Granville, Shuguang Li and Sun Qi,
On the number of solutions to the equation
a1/x1 + .... + an/xn = 0 mod 1,
Sichuan Daxue Xuebao, 32 (1995), 243-248.
- Andrew Granville, Richard Mollin and Hugh C. Williams
An upper bound on the least inert prime in a real quadratic field
Canadian Journal of Mathematics 52 (2000), 369-380.
to
Andrew Granville's Homepage