Andrew Granville's
expository papers

Topics: Additive Combinatorics, Computational number theory, distribution of primes,
classical analytic and algebraic number theory, arithmetic geometry, biographies,
binomial coefficients, Diophantine equations and reviews.


Additive Combinatorics
with Javier Cilleruelo
  • Article
  • Lattice points on circles, squares in arithmetic progressions, and sumsets of squares
    Proceedings, Additive Combinatorics workshop, Montreal 2006
  • Article
  • An Introduction to Additive Combinatorics
    Proceedings, Additive Combinatorics workshop, Montreal 2006


    Computational number theory

  • Article and AMS Review
  • It is easy to determine whether a given integer is prime,
    Bulletin of the American Mathematical Society 42 (2005), pages 3-38
  • Article
  • Smooth numbers: Computational number theory and beyond
    MSRI workshop , proceedings
  • Article and AMS Review
  • Primality testing and Carmichael numbers
    Notices of the American Mathematical Society
    vol 39 (1992), pages 696--700


    Distribution of primes

  • Article
  • Analytic Number Theory,
    Princeton Companion to Mathematics
  • Article
  • Prime number patterns
    American Mathematical Monthly
  • Article
  • A good new millenium for the primes
    The Madrid Intelligencer
    (2006) pages 32-36
    with Greg Martin
  • Article and in Spanish
  • Prime number races / Carreras de numeros primos
    American Mathematical Monthly and
    La Gaceta de le Real Sociedad Matematica Espanola
    vol 8.1 (2005) pages 197-240
  • Article and in French
  • Prime Possibilities and Quantum Chaos, Emissary (Spring 2002) and
    Nombres premiers et chaos quantique,
    Gazette des Mathematiciens vol 97 (2003) pages 29--44
  • Article and AMS Review
  • Unexpected irregularities in the distribution of prime numbers
    Proceedings of the International Congress of Mathematicians (Zürich, 1994), vol 1, 2, pages 388--399.
  • Article and AMS Review
  • Harold Cramér and the distribution of prime numbers
    Scandanavian Actuarial J., 1 (1995), pages 12- 28
  • Article
  • International team shows that primes can be found in surprising places
    Resonance, 3 (1998) pages 71--72


    Classical analytic number theory

    with Zeev Rudnick
  • Article
  • Uniform distribution
    in Equidistribution in number theory, An introduction
    (2007) pages 1-13


    Classical algebraic number theory

  • Article
  • The Fundamental Theorem of Arithmetic
    in Mathematics and Culture


    Arithmetic Geometry

    with Tom Tucker
  • Article and AMS Review
  • It's as easy as abc
    Notices of the American Mathematical Society, vol 49 (2002), pages 1224-1231
  • Article
  • The distribution of roots of a polynomial
    in Equidistribution in number theory, An introduction
    (2007) pages 93-102
    with Zeev Rudnick
  • Article
  • Torsion points on curves
    in Equidistribution in number theory, An introduction
    (2007) pages 85-92


    Biographies

  • Article
  • Computation at the heart of mathematics
    Celebrating the work of David Boyd
    PIMS magazine, 9.1 (Summer 2005)
  • Article
  • On the research contributions of Hugh C. Williams
    "High Primes and Misdemeanours: Lectures in honour of the 60th birthday of Hugh Cowie Williams"
    Fields Institute Communications 41 (2004) pages 197--216
  • Article
  • Paulo Ribenboim on his retirement
    "Advances in Number Theory" (ed. F.Q. Gouvea and N. Yui)
    New York, Oxford University Press, (1993) pages 469--478


    Binomial Coefficients

  • Article and AMS Review
  • Arithmetic Properties of Binomial Coefficients I: Binomial coefficients modulo prime powers
    Canadian Mathematical Society Conference Proceedings, vol 20 (1997) pages 253-275
  • Article and AMS Review;
    Corrigendum and AMS Review
  • Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle
    American Mathematical Monthly, vol 99 (1992) pages 318-331;
    (Corrigendum) vol 104 (1997) pages 848-851


    Diophantine Equations

  • Article
  • The latest on Catalan's Conjecture
    Focus, 13 (4) (April 2001) pages 3--4
    with Michael Monagan
  • Article
  • The Status of Fermat's Last Theorem -- mid 1994
    Maple in Mathematics and Sciences (1994) pages 6--9
    with Keith Devlin and Fernando Gouvea
  • Article
  • Fermat's Last Theorem, a Theorem at Last
    Focus 13 (August 1993) pages 3--4
    with Ian Katz
  • Article
  • The number's up for maths' greatest riddle
    The Guardian, section 2, (24th June 1993) pages 1--3


    Reviews

  • Article
  • Review of ``Notes on Fermat's Last Theorem'' by Alf van der Poorten
    American Mathematical Monthly, 106 (1999), pages 177--181.
  • Article
  • Review of BBC's Horizon Program,``Fermat's Last Theorem''
    Notices of the American Mathematical Society, 44 (1997), pages 26--28.
    with Nigel Boston
  • Article
  • Review of ``The World's Most Famous Math Problem'' by Marilyn vos Savant
    American Mathematical Monthly, 102 (1995), pages 470--473.