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Constructing Weyl group multiple Dirichlet series

Author(s): Gautam Chinta; Paul E. Gunnells
Journal: J. Amer. Math. Soc. 23 (2010), 189-215.
MSC (2000): Primary 11F66, 11M41; Secondary 11F37, 11F70, 22E99
Posted: July 31, 2009
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Abstract: Let $ \Phi$ be a reduced root system of rank $ r$. A Weyl group multiple Dirichlet series for $ \Phi$ is a Dirichlet series in $ r$ complex variables $ s_1,\dots,s_r$, initially converging for $ {Re}(s_i)$ sufficiently large, that has meromorphic continuation to $ {\mathbb{C}}^r$ and satisfies functional equations under the transformations of $ {\mathbb{C}}^r$ corresponding to the Weyl group of $ \Phi$. A heuristic definition of such a series was given by Brubaker, Bump, Chinta, Friedberg, and Hoffstein, and they have been investigated in certain special cases by others.

In this paper we generalize results by Chinta and Gunnells to construct Weyl group multiple Dirichlet series by a uniform method and show in all cases that they have the expected properties.

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Additional Information:

Gautam Chinta
Affiliation: Department of Mathematics, The City College of CUNY, New York, New York 10031
Email: chinta@sci.ccny.cuny.edu

Paul E. Gunnells
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
Email: gunnells@math.umass.edu

DOI: 10.1090/S0894-0347-09-00641-9
PII: S 0894-0347(09)00641-9
Keywords: Weyl group multiple Dirichlet series, Fourier coefficients of Eisenstein series, Weyl character formula, metaplectic groups
Received by editor(s): March 11, 2008
Posted: July 31, 2009
Additional Notes: Both authors thank the NSF for support.
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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