Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen 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. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
The life and work of Gustav Lejeune Dirichlet (1805-1859) by J. Elstrodt An overview of Manin's conjecture for del Pezzo surfaces by T. D. Browning The density of integral solutions for pairs of diagonal cubic equations by J. Bruden and T. D. Wooley Second moments of $GL 2$ automorphic $L$-functions by A. Diaconu and D. GOldfeld CM Points and weight 3/2 modular forms by J. Funke The path to recent progress on small gaps between primes by D. A. Goldston, J. Pintz, and C. Y. Yildrim Negative values of truncations to $L(1,\chi)$ by A. Granville and K. Soundarajan Long arithmetic progressions of primes by B. Green Heegner points and non-vanishing of Rankin/Selberg $L$-functions by P. Michel and A. Venkatesh Singular moduli generating functions for modular curves and surfaces by K. Ono Rational points of bounded height on threefolds by P. Salberger Reciprocal geodesics by P. Sarnak The fourth moment of Dirichlet $L$-functions by K. Soundarajan The Gauss class-number problems by H. M. Stark.