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Twisted Weyl group multiple Dirichlet series over the rational function field

Banff International Research Station for Mathematical Innovation and Discovery

Similar to zeta functions associated to algebraic function fields, Weyl group multiple Dirichlet series associated to algebraic function fields are rational functions in several variables. The denominators of these rational functions are known, but the numerators are not well understood. Like zeta functions, we expect the coefficients of the numerators to encode information about the arithmetic of the defining curve. As a step toward understanding this relationship, in this talk we describe the support of Weyl group multiple Dirichlet series defined over the rational function field ${\mathbb{F}}_q(t)$. In particular, we show that up to a variable change, all such series can be expressed as a finite sum of simpler local series, which act analogue to Euler factors in the construction of the global object.

Mathematics; Number theory; Quantum theory

video/mp4

Author affiliation: Dickinson College

2017-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60435

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/