A CONVERSE THEOREM FOR DOUBLE DIRICHLET SERIES By NIKOLAOS DIAMANTIS and DORIAN GOLDFELD

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions Nikolaos Diamantis and Dorian Goldfeld

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions Nikolaos Diamantis and Dorian Goldfeld

A Converse Theorem for Double Dirichlet Series and Shintani Zeta Functions

The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions [13] which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL(2). The converse theorem we prove will apply to a very general family of double Dirichlet series which...

Multiple Dirichlet Series and Moments of Zeta and L–functions

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments o...

Natural Boundaries and the Correct Notion of Integral Moments of L–functions

It is shown that a large class of multiple Dirichlet series which arise naturally in the study of moments of L–functions have natural boundaries. As a remedy we consider a new class of multiple Dirichlet series whose elements have nice properties: a functional equation and meromorphic continuation. We believe this class reveals the correct notion of integral moments of L–functions. §