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           Analytic Number Theory: A Tribute to Gauss and Dirichlet

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Type.................: Ebook

Part Size............: 2,697,481 bytes









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Posted by............: ~tqw~



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Articles in this volume are based on talks given at the Gauss-Dirichlet 

Conference held in Gottingen on June 20, 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.



Table Of Contents



Foreword vii

The Life and Work of Gustav Lejeune Dirichlet (1805.1859) 1

An overview of Maninfs conjecture for del Pezzo surfaces 39

The density of integral solutions for pairs of diagonal cubic equations 57

Second moments of GL2 automorphic L-functions 77

CM points and weight 3/2 modular forms 107

The path to recent progress on small gaps between primes 129

Negative values of truncations to L(1, ƒÔ) 141

Long arithmetic progressions of primes 149

Heegner points and non-vanishing of Rankin/Selberg L-functions 169

Singular moduli generating functions for modular curves and surfaces 185

Rational points of bounded height on threefolds 207

Reciprocal Geodesics 217

The fourth moment of Dirichlet L-functions 239

The Gauss Class-Number Problems 247



Product Details



    * ISBN: 0821843079

    * ISBN-13: 9780821843079

    * Format: Paperback, 256pp

    * Publisher: American Mathematical Society

    * Pub. Date: September 2007



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