A converse theorem for double Dirichlet series and Shintani zeta functions

Diamantis, Nikolaos; Goldfeld, Dorian

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: Jun 30, 2016
• 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
• Contract Date: Jun 30, 2016