Andrew Granville's
publications in
algebraic number theory

Topics: Applications of Faltings' Theorem, Generalized Fermat equations, Class number of cyclotomic fields,
the abc-conjecture, Finite fields, Elliptic Curves, and Fermat's Last Theorem.


Applications of Faltings' Theorem
with Enrico Bombieri and Janos Pintz
  • Article and AMS Review
    		• Squares in arithmetic progressions
    Duke Mathematical Journal,  vol. 66 (1992) pages 165-204
    with Henri Darmon
  • Article and AMS Review
    		• On the equations zm=F(x,y) and Axp+Byq =Czr
    Bulletin on the London Mathematical Society, 27 (1995) pages 515-543 

  • Article and AMS Review
    		• The set of exponents, for which Fermat's Last Theorem is true, has density one
    Comptes Rendus de l'Académie des Sciences du Canada, vol 7 (1985) pages 55-60


    Generalized Fermat equations

    with Henri Darmon
  • Article and AMS Review
    		• On the equations zm=F(x,y) and Axp+Byq =Czr
    Bulletin on the London Mathematical Society, 27 (1995) pages 515-543 
  • Article and AMS Review
    		• On the number of solutions to the generalized Fermat equation
    'Number Theory', Proceedings of CNTA IV (K. Dilcher, ed.) CMS Conference Proceedings, 15 (1995) pages 197-207
  • Article and AMS Review
    		• Finding integers k for which a given Diophantine Equation has no solution in kth powers of integers
    Acta Arithmetica, vol 60 (1992) pages 203-212


    Class number of cyclotomic fields

    with Ernest S. Croot III
  • Article and AMS Review
    		• Unit fractions and the class number of a cyclotomic field
    Journal of the London Mathematical Society , vol 66 (2002) pages 579-591
    with Gilbert Fung and Hugh C. Williams
  • Article and AMS Review
    		• Computation on the first factor of the class number of cyclotomic fields
    Journal of Number Theory, vol. 42 (1992) pages 297-312
  • Article and AMS Review
    		• On the size of the first factor of the class number of a cyclotomic field
    Inventiones Mathematicae, vol 100 (1990) pages 321-338


    abc-conjecture

    with Pam Cutter and Tom Tucker
  • Article and AMS Review
    		• The number of fields generated by the square root of values of a given polynomial
    Canadian Mathematical Bulletin, vol 46 (2003) pages 71-79
    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


    Finite fields

    with Brad Brock
  • Article and AMS Review
    		• More points on curves over finite fields than expected
    Finite Fields and their Applications, vol 7 (2001) pages 70-91
    with Shuguang Li and Sun Qi
  • Article and AMS Review
    		•  On the number of solutions to the equation a_1/x_1 + ... + a_n/x_n = 0 mod 1
    Sichuan Daxue Xuebao, vol 32 (1995) pages 243-248


    Elliptic Curves

  • Article and AMS Review
    		• 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, 228 (1995) pages 81-100


    Fermat's Last Theorem

  • Article and AMS Review
    		• The Kummer-Wieferich-Skula criteria for the first case of Fermat's Last Theorem
    Advances in Number Theory (ed. F. Q. Gouvea and N. Yui), (New York: Oxford U. Press, 1993), pages 479-498
    with Greg J. Fee
  • Article and AMS Review
    		• The prime factors of Wendt's binomial circulant determinant
    Mathematics of Computation, vol 57 (1991) pages 839-848
  • Article and AMS Review
    		• Some conjectures related to Fermat's Last Theorem
    Number Theory (ed. R.A. Mollin), (New York: de Gruyter, 1990), pages 177-192

  • Article and AMS Review
    		• Some conjectures in Analytic Number Theory and their connection with Fermat's Last Theorem
    Analytic Number Theory (ed. B.C. Berndt, H.G. Diamond, H. Halberstam, A. Hildebrand), (Boston: Birkhauser,1990), page 311-326
    with Michael B. Monagan
  • Article and AMS Review
    		• 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, vol 306 (1988) pages 329-359
    with Barry J. Powell
  • Article and AMS Review
    		• On Sophie Germain type criteria for Fermat's Last Theorem
    Acta Arithmetica, vol 50 (1988) pages 265-277
  • Article and AMS Review

    • Sophie Germain's Theorem for prime pairs p,  6p+1
    Journal  of Number Theory , vol 27 (1987) pages 63-72

  • Article and AMS Review

    • Powerful numbers and Fermat's Last Theorem
    Comptes Rendus de l'Académie des Sciences du Canada, vol 8 (1986) pages 215-218

  • Article and AMS Review

    • On Krasner's criteria for the first case of Fermat's Last Theorem
    Manuscripta Mathematica,  vol 56 (1986) pages 67-70

  • Article and AMS Review
    		• Refining the conditions on the Fermat quotient
    Mathematical Proceedings of the Cambridge Philosophical Society, vol 98 (1985) pages 5-8

  • Article and AMS Review
    		• The set of exponents, for which Fermat's Last Theorem is true, has density one
    Comptes Rendus de l'Académie des Sciences du Canada, vol 7 (1985) pages 55-60