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Weyl group multiple Dirichlet series of type A 2

In: Number Theory, Analysis and Geometry

Author

Listed:
  • Gautam Chinta

    (The City College of CUNY, Department of Mathematics)

  • Paul E. Gunnells

    (University of Massachusetts, Department of Mathematics and Statistics)

Abstract

A Weyl group multiple Dirichlet seriesis a Dirichlet series in several complex variables attached to a root system Φ. The number of variables equals the rank rof the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group Wof Φ. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n th order Gauss sums attached to the root system of type A 2. The basic technique is that of [11, 10]; namely, we construct a rational function in rvariables invariant under a certain action of W, and use this to build a “local factor” of the global series.

Suggested Citation

  • Gautam Chinta & Paul E. Gunnells, 2012. "Weyl group multiple Dirichlet series of type A 2," Springer Books, in: Dorian Goldfeld & Jay Jorgenson & Peter Jones & Dinakar Ramakrishnan & Kenneth Ribet & John Tate (ed.), Number Theory, Analysis and Geometry, edition 127, pages 125-142, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-1260-1_6
    DOI: 10.1007/978-1-4614-1260-1_6
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