A converse theorem for double Dirichlet series and Shintani zeta functions

Diamantis, Nikolaos and Goldfeld, Dorian (2014) A converse theorem for double Dirichlet series and Shintani zeta functions. Journal of the Mathematical Society of Japan, 66 (2). pp. 449-477. ISSN 1881-1167

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Abstract

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 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 we now define.

Item Type: Article
Keywords: Double Dirichlet series, Eisenstein series, converse theorems, forms of half-integral weight
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.2969/jmsj/06620449
Depositing User: Diamantis, Dr Nikolaos
Date Deposited: 30 Jun 2016 11:49
Last Modified: 26 Sep 2016 15:12
URI: http://eprints.nottingham.ac.uk/id/eprint/34545

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