Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

ISBN-10:
0821839632
ISBN-13:
9780821839638
Pub. Date:
11/22/2006
Publisher:
American Mathematical Society

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Overview

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet series, and on developments in the allied fields of automorphic forms and analytic number theory.

Product Details

ISBN-13: 9780821839638
Publisher: American Mathematical Society
Publication date: 11/22/2006
Series: Proceedings of Symposia in Pure Mathematics Series , #75
Edition description: New Edition
Pages: 303
Product dimensions: 7.20(w) x 10.20(h) x 0.90(d)

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