Journal of the Mathematical Society of Japan

A converse theorem for double Dirichlet series and Shintani zeta functions

Nikolaos DIAMANTIS and Dorian GOLDFELD

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Abstract

A converse theorem for double Dirichlet series is established. As an application, we show that certain zeta functions introduced by Shintani are actually Weyl group multiple Dirichlet series associated to metaplectic Eisenstein series on $GL(2)$.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 2 (2014), 449-477.

Dates
First available in Project Euclid: 23 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1398258180

Digital Object Identifier
doi:10.2969/jmsj/06620449

Mathematical Reviews number (MathSciNet)
MR3201822

Zentralblatt MATH identifier
1311.11043

Subjects
Primary: 11F68: Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series
Secondary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values 11F37: Forms of half-integer weight; nonholomorphic modular forms

Keywords
double Dirichlet series Eisenstein series converse theorems forms of half-integral weight

Citation

DIAMANTIS, Nikolaos; GOLDFELD, Dorian. A converse theorem for double Dirichlet series and Shintani zeta functions. J. Math. Soc. Japan 66 (2014), no. 2, 449--477. doi:10.2969/jmsj/06620449. https://projecteuclid.org/euclid.jmsj/1398258180


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References

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