A CONVERSE THEOREM FOR DOUBLE DIRICHLET SERIES

We prove that a certain vector valued double Dirichlet series satisfying appropriate functional equations is a Mellin transform of a vector valued metaplectic Eisenstein series. We establish an analogous result for scalar double Dirichlet series of the type studied by Siegel.

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Bibliographic Details
Published inAmerican journal of mathematics Vol. 133; no. 4; pp. 913 - 938
Main Authors Diamantis, Nikolaos, Goldfeld, Dorian
Format Journal Article
LanguageEnglish
Published Baltimore, MD Johns Hopkins University Press 01.08.2011
Subjects
Algebra
Complex numbers
Difference and functional equations, recurrence relations
Dirichlet problem
Exact sciences and technology
Finite differences and functional equations
General mathematics
General, history and biography
Infinity
Integers
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematical vectors
Mathematics
Mellin transforms
Numerical analysis
Numerical analysis. Scientific computation
Scalars
Sciences and techniques of general use
Series convergence
Theorems
Double series
Eisenstein series
Dirichlet series
Vector
Functional equation
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Summary:We prove that a certain vector valued double Dirichlet series satisfying appropriate functional equations is a Mellin transform of a vector valued metaplectic Eisenstein series. We establish an analogous result for scalar double Dirichlet series of the type studied by Siegel.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2011.0024