Clay Mathematics Proceedings 2007; 256 pp; softcover Volume: 7 ISBN10: 0821843079 ISBN13: 9780821843079 List Price: US$50 Member Price: US$40 Order Code: CMIP/7
 Articles in this volume are based on talks given at the GaussDirichlet Conference held in Göttingen on June 2024, 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 copublished 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 (18051859)
 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 nonvanishing 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 classnumber problems
