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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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 $GL(2)$.

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

First available in Project Euclid: 23 April 2014

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Zentralblatt MATH identifier

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

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


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.

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