Vol 7. Analytic Number Theory: A Tribute to Gauss and Dirichlet
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 Lfunctions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.
Contents

The life and work of Gustav Lejeune Dirichlet (18051859)
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 GL_{2} automorphic Lfunctions
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 nonvanishing of Rankin/Selberg Lfunctions
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 Lfunctions
K. Soundararajan  The Gauss classnumber problems
H. M. Stark
CMI/AMS publication. 256 pp., Softcover, List: $50, AMS Members: $40. Order code: CMIP/7. Students: $40. 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