Analytic Number Theory: A Tribute to Gauss and Dirichlet

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CMI/AMS publication. 256 pp., Softcover, List: $49, AMS Members: $39. Order code: CMIP/7. Students: $39. Order code: CLAY MATH. Available at the AMS bookstore

Editors: William Duke and Yuri Tschinkel

Authors: T.D. Browning, Jörg Brüdern, Adrian Diaconu, Jürgen Elstrodt, Jens Funke, Dorian Goldfeld, D.A. Goldston, Andrew Granville, Ben Green, Philippe Michel, Ken Ono, J. Pintz, Per Salberger, Peter Sarnak, K. Soundararajan, H. M. Stark, Akshay Venkatesh, Trevor Wooley, C.Y. Yildirim

Description

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet.

The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of L-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.

Table of Contents

• The life and work of Gustav Lejeune Dirichlet (1805-1859)
  J. Elstrodt
• An overview of Manin's conjecture for del Pezzo surfaces
  T. D. Browning
• The density of integral solutions for pairs of diagonal cubic equations
  J. Brüdern and T. D. Wooley
• Second moments of GL₂ automorphic L-functions
  A. Diaconu and D. Goldfeld
• CM points and weight 3/2 modular forms
  J. Funke
• The path to recent progress on small gaps between primes
  D. A. Goldston, J. Pintz, and C. Y. Yildirim
• Negative values of truncations to L(1,X)
  A. Granville and K. Soundararajan
• Long arithmetic progressions of primes
  B. Green
• Heegner points and non-vanishing of Rankin/Selberg L-functions
  P. Michel and A. Venkatesh
• Singular moduli generating functions for modular curves and surfaces
  K. Ono
• Rational points of bounded height on threefolds
  P. Salberger
• Reciprocal geodesics
  P. Sarnak
• The fourth moment of Dirichlet L-functions
  K. Soundararajan
• The Gauss class-number problems
  H. M. Stark

Sample Pages

• The life and work of Gustav Lejeune Dirichlet (1805-1859)
• An overview of Manin's conjecture for del Pezzo surfaces
• The density of integral solutions for pairs of diagonal cubic equations
• Second moments of GL₂ automorphic L-functions
• CM points and weight 3/2 modular forms
• The path to recent progress on small gaps between primes
• Negative values of truncations to L(1,X)
• Long arithmetic progressions of primes
• Heegner points and non-vanishing of Rankin/Selberg L-functions
• Singular moduli generating functions for modular curves and surfaces
• Rational points of bounded height on threefolds
• Reciprocal geodesics
• The fourth moment of Dirichlet L-functions
• The Gauss class-number problems

PDF file available on the CMI online library