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A converse theorem for double Dirichlet series and Shintani zeta functions

Diamantis, Nikolaos; Goldfeld, Dorian

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Authors

Dorian Goldfeld



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.

Citation

Diamantis, N., & Goldfeld, D. (2014). A converse theorem for double Dirichlet series and Shintani zeta functions. https://doi.org/10.2969/jmsj/06620449

Journal Article Type Article
Acceptance Date Sep 9, 2013
Publication Date Apr 1, 2014
Deposit Date Jun 30, 2016
Publicly Available Date Mar 29, 2024
Journal Journal of the Mathematical Society of Japan
Electronic ISSN 1881-1167
Peer Reviewed Peer Reviewed
Volume 66
Issue 2
DOI https://doi.org/10.2969/jmsj/06620449
Keywords Double Dirichlet series, Eisenstein series, converse theorems, forms of half-integral weight
Public URL https://nottingham-repository.worktribe.com/output/996286
Publisher URL http://projecteuclid.org/euclid.jmsj/1398258180

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