Duke W., Tschinkel Y. (eds.) Analytic Number Theory. A Tribute to Gauss and Dirichlet

Clay Mathematics Institute, 2007. - 256 pages
ISBN: 0821843079Articles 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.Elstrodt The life and work of Gustav Lejeune Dirichlet
Browning An overview of Manin's conjecture for del Pezzo surfaces
Brüdern, Wooley The density of integral solutions for pairs of diagonal cubic equations
Diaconu, Goldfeld Second moments of GL2 automorphic L-functions
Funke CM points and weight 3/2 modular forms
Goldston, Pintz, Yildirim The path to recent progress on small gaps between primes
Granville, Soundararajan Negative values of truncations to L(1,X)
Green Long arithmetic progressions of primes
Michel, Venkatesh Heegner points and non-vanishing of Rankin/Selberg L-functions
Ono Singular moduli generating functions for modular curves and surfaces
Salberger Rational points of bounded height on threefolds
Sarnak Reciprocal geodesics
Soundararajan The fourth moment of Dirichlet L-functions
Stark The Gauss class-number problems