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Analytic Number Theory: A Tribute to Gauss and Dirichlet
Edited by: William Duke, University of California Los Angeles, CA, and Yuri Tschinkel, Courant Institute - New York University, NY
A co-publication of the AMS and Clay Mathematics Institute.
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Clay Mathematics Proceedings
2007; 256 pp; softcover
Volume: 7
ISBN-10: 0-8218-4307-9
ISBN-13: 978-0-8218-4307-9
List Price: US$50
Member Price: US$40
Order Code: CMIP/7
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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.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

  • J. Elstrodt -- The life and work of Gustav Lejeune Dirichlet (1805-1859)
  • T. D. Browning -- An overview of Manin's conjecture for del Pezzo surfaces
  • J. Brüdern and T. D. Wooley -- The density of integral solutions for pairs of diagonal cubic equations
  • A. Diaconu and D. Goldfeld -- Second moments of \(GL_2\) automorphic \(L\)-functions
  • J. Funke -- CM points and weight 3/2 modular forms
  • D. A. Goldston, J. Pintz, and C. Y. Yıldırım -- The path to recent progress on small gaps between primes
  • A. Granville and K. Soundararajan -- Negative values of truncations to \(L(1,\chi)\)
  • B. Green -- Long arithmetic progressions of primes
  • P. Michel and A. Venkatesh -- Heegner points and non-vanishing of Rankin/Selberg \(L\)-functions
  • K. Ono -- Singular moduli generating functions for modular curves and surfaces
  • P. Salberger -- Rational points of bounded height on threefolds
  • P. Sarnak -- Reciprocal geodesics
  • K. Soundararajan -- The fourth moment of Dirichlet \(L\)-functions
  • H. M. Stark -- The Gauss class-number problems
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