## Constructing Weyl group multiple Dirichlet series

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- by Gautam Chinta and Paul E. Gunnells
- J. Amer. Math. Soc.
**23**(2010), 189-215 - DOI: https://doi.org/10.1090/S0894-0347-09-00641-9
- Published electronically: 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 $\mathrm {Re}(s_i)$ 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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## Bibliographic Information

**Gautam Chinta**- Affiliation: Department of Mathematics, The City College of CUNY, New York, New York 10031
- MR Author ID: 679536
- 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
- Received by editor(s): March 11, 2008
- Published electronically: July 31, 2009
- Additional Notes: Both authors thank the NSF for support.
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**23**(2010), 189-215 - MSC (2000): Primary 11F66, 11M41; Secondary 11F37, 11F70, 22E99
- DOI: https://doi.org/10.1090/S0894-0347-09-00641-9
- MathSciNet review: 2552251