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
Official URL: http://projecteuclid.org/euclid.jmsj/1398258180
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.
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