Andrew Granville's
publications in
combinatorial number theory

Topics: Squares, Additive combinatorics, Binomial coefficients, Riemann zeta-function,
Bernoulli polynomials and other topics.


Squares
with John Selfridge
  • Article and AMS Review
    		• Product of integers in an interval, modulo squares
    Electronic Journal of Combinatorics, vol 8(1) R5 (2001)
    with Enrico Bombieri and Janos Pintz
  • Article and AMS Review
    		• Squares in arithmetic progressions
    Duke Mathematical Journal,  vol. 66 (1992) pages 165-204


    Additive Combinatorics

    with F. Roesler
  • Article and AMS Review
    		• The set of differences of a given set
    American Mathematical Monthly, vol 106 (1999) pages 338-344


    Binomial Coefficients


  • Website
    		• Arithmetic properties of Binomial Coefficients
    (last update 1999)

  • Article and AMS Review
    		• On the scarcity of powerful binomial coefficients
    Mathematika, vol 46 (1999) pages 397-410
  • Article and AMS Review
    		• Correction to: "Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle"
    American Mathematical Monthly, vol 104 (1997) pages 848-851
  • 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
    with Olivier Ramaré
  • Article and AMS Review
    		• Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients 
    Mathematika, vol 43 (1996) pages 73-107
  • Article 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
    with Yiliang Zhu
  • Article and AMS Review
    		• Representing binomial coefficients as sums of squares
    American Mathematical Monthly, vol 97 (1990) pages 486-493


    Riemann zeta-function

    with Gert Almkvist
  • Article and AMS Review
    		• Borwein and Bradley's Apéry-like formulae for zeta(4n+3)
    Experimental Mathematics, vol 8 (1999) pages 197-204
  • Article and AMS Review
    		• A Decomposition of Riemann's Zeta-Function
    London Mathematical Society Lecture Notes (Proceedings of the Kyoto Conference)
    vol 247 (1997) pages 95-101


    Bernoulli polynomials

    with Zhi-Wei Sun
  • Article and AMS Review
    		• Special Values of Bernoulli polynomials
    Pacific Journal of Mathematics, vol 32 (1996) pages 243-248
    with Herb S. Shank
  • Article and AMS Review
    		• Defining Bernoulli polynomials in Z/pZ (A generic regularity condition)
    Proceeding of the American Mathematical Society, vol 108 (1990) pages 637-640


    Other topics

    with Ken Ono
  • Article and AMS Review
    		• Defect zero p-blocks for finite simple groups
    Transactions of the American Mathematical Society, vol 348 (1996) pages 331-347
    with Neil J. Calkin
  • Article and AMS Review
    		• On the number of co-prime-free sets Number Theory: New Yòrk Seminar 1991-1995 (D. Chudnovsky, G. Chudnovsky and M. Nathanson, eds) Springer-Verlag, pages 9-18