Andrew Granville's
publications in
analytic number theory

Topics: Character Sums, Multiplicative functions, L(1,chi) values, abc-conjecture, Exponential sums,
Smooth numbers, Distribution of primes, Goldbach conjecture, Residue Races, Other topics.


Character sums
with K. Soundararajan
  • Article and AMS Review
    		• Large Character Sums
    Journal of the American Mathematical Society , vol 14 (2001) pages 365-397.


    Multiplicative functions

    with K. Soundararajan
  • Article and AMS Review
    		• The number of unsieved integers up to x
    Acta Arithmetica, 115 (2004) pages 305-328.
    with K. Soundararajan
  • Article and AMS Review
    		• Decay of mean-values of multiplicative functions
    Canadian Journal of Mathematics , vol 55 (2003) pages 1191-1230
    with K. Soundararajan
  • Article and AMS Review
    		• The spectrum of multiplicative functions
    Annals of Mathematics , vol 153 (2001) pages 407-470
    with K. Soundararajan
  • Article and AMS Review
    		• Motivating the multiplicative spectrum
    Topics in Number Theory, (S.D. Ahlgren et al., eds.), Netherlands: Kluwer (1999) pages 1-5


    L-functions at the edge of the critical strip

    with K. Soundararajan
  • Article, and AMS Review

    • Distribution of values of  L(1,chid).
    Geometric and Functional Analysis, vol 13 (2003) pages 992-1028
    ( Errata ) vol 14 (2004) pages 245-246

    with K. Soundararajan
  • Article and AMS Review
    		• Upper bounds for |L(1,chi)|
    Quarterly Journal of Mathematics, vol 53 (2002) pages 265-284
    with Brian Conrey, K. Soundararajan and Bjorn Poonen
  • Article and AMS Review
    		• Zeros of Fekete polynomials
    Annales de l'Institut Fourier (Grenoble), vol 50 (2000) pages 865--889


    abc-conjecture and analytic number theory

    with Harold M. Stark
  • Article and AMS Review
    		• ABC implies no "Siegel Zeroes'' for L-functions of characters with negative discriminant
    Inventiones Mathematicae, vol 139 (2000) pages 509-523
  • Article and AMS Review
    		• ABC allows us to can count squarefrees
    International Mathematical Research Notices, vol 19 (1998) pages 991-1009


    Exponential sums

    with Joerg Brudern, Alberto Perelli, Bob Vaughan and Trevor Wooley
  • Article and AMS Review
    		• On the exponential sum over k-free numbers
    Philosophical Transactions of the Royal Society, vol 356 (1998) pages 739-761
    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


    Smooth numbers

    with K. Soundararajan
  • Article and AMS Review
    		• Large Character Sums
    Journal of the American Mathematical Society , vol 14 (2001) pages 365-397.
  • Article and AMS Review
    		• On integers, without large prime factors, in arithmetic progressions I
    Acta Mathematica, vol 170 (1993) pages 255-273
    with John B. Friedlander
  • Article and AMS Review
    		• Smoothing "smooth" numbers
    Philosophical Transactions of the Royal Society, vol 345 (1993) pages 339-348
  • Article and AMS Review
    		• On integers, without large prime factors, in arithmetic progressions II
    Philosophical Transactions of the Royal Society, vol 345 (1993) pages 349-362
  • Article and AMS Review
    		• The lattice points of an n-dimensional tetrahedron
    Aequationes Mathematicae, vol 41 (1991) pages 234-241

  • Article and AMS Review
    		• On pairs of coprime integers with no large prime factors
    Expositiones Mathematicae, vol. 9 (1991) pages 335-350
  • Article and AMS Review
    		• On positive integers <=x with prime factors <= t log x. 
    Number Theory and Applications (ed R.A. Mollin) (Kluwer, NATO ASI, 1989), pages 403-422


    Distribution of primes

    with Greg Martin
  • Article
    		• Prime number races
    American Mathematical Monthly
    vol 113 (2006) pages 1-33
    with Richard Mollin
  • Article and AMS Review
    		• Rabinowicz revisited
    Acta Arithmetica , vol 96 (2001) pages 139-153
    with Takashi Agoh and Paul Erdos
  • Article and AMS Review
    		• Primes at a (somewhat lenghty) glance
    American Mathematical Monthly, vol 104 (1997) pages 943-945
  • Article and AMS Review
    		• Harold Cramér and the distribution of prime numbers
    Scandanavian Actuarial J., 1 (1995) pages 12- 28
  • 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
    		• Solution to a problem of Bombieri
    Atti della Accademia Nazionale dei Lincei, vol. 9 (1993) pages 181-183
    with John B. Friedlander
  • Article and AMS Review
    		• Limitations to the equi-distribution of primes III
    Compositio Mathematicae, vol 81 (1992) pages 19-32
  • Article and AMS Review
    		• On elementary proofs of the Prime Number Theorem for arithmetic progressions, without characters
    Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), (Univ. Salerno: Salerno, Italy, 1992) pages 157-194
    with John B. Friedlander
  • Article and AMS Review
    		• Relevance of the residue class to the abundance of primes
    Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), (Univ. Salerno: Salerno, Italy, 1992) pages 95-104
  • Article and AMS Review
    		• A note of sums of primes
    Canadian Mathematical Bulletin,  vol 33 (1991) pages 452-454
    with John B. Friedlander, Adolf Hildebrand & Helmut Maier
  • Article and AMS Review
    		• Oscillation theorems for primes in arithmetic progressions and for sifting functions
    Journal of the American Mathematical Society, vol 4 (1991) pages 25-86
    with John B. Friedlander
  • Article and AMS Review

    • Limitations to the equi-distribution of primes IV
    Proceedings of the Royal Society (Series A), vol 435 (1991) pages 197-204
    with Carl Pomerance
  • Article and AMS Review
    		• On the least prime in certain arithmetic progressions
    Journal of the London Mathematical Society, vol. 41 (1990) pages 193-200
    with John B. Friedlander
  • Article and AMS Review
    		• Limitations to the equi-distribution of primes I
    Annals of Mathematics, vol. 129 (1989) pages 363-382

  • Article and AMS Review
    		• Least primes in arithmetic progressions
    Théorie des nombres / Number Theory (ed. J.-M. De Koninck and C. Lévesque) (de Gruyter: New York, 1989), pages 306-321


    Residue Races

    with Peter and Daniel Shiu
  • Article
    		• Residue races
    Ramanujan Journal
    vol 11 (2006) pages 67-94
    with Igor Shparlinski and Alexandru Zaharescu
  • Articleand AMS Review
    		• On the Distribution of Rational Functions Along a Curve over F_p and Residue Races
    Journal of Number Theory
    vol 112 (2005) pages 216-237


    Goldbach conjecture

    with Jean-Marc Deshouillers, Wladyslaw Narkiewica and Carl Pomerance
  • Article and AMS Review
    		• An upper bound in Goldbach's problem

    Mathematics of Computation, vol 61 (1993) pages 209-213

    with J. Van de Lune and Herman te Riele
  • Article and AMS Review
    		• Checking the Goldbach Conjecture on a vector computer
    Number Theory and Applications (ed R.A. Mollin) (Kluwer, NATO ASI, 1989), pages 423-434


    Others

    with Jorge Jiménez-Urroz
  • Article and AMS Review
    		• The least common multiple and lattice points on hyperbolas
    Quarterly Journal of Mathematics (Oxford), vol 51 (2000) pages 343--352
    with K. Soundararajan
  • Article and AMS Review
    		• A binary additive problem of Erdös and the order of 2 mod p2
    Ramanujan Journal, vol 2(1998) pages 283-298
    with Paul Erdos, Carl Pomerance and Claudia Spiro

  • Article and AMS Review
    		• On the normal behavior of the iterates of some arithmetic functions
    Analytic Number Theory (ed. B.C. Berndt, H.G. Diamond, H. Halberstam, A. Hildebrand), (Boston: Birkhauser, 1990), page 165-204