Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$
Number Theory
2019-02-20 v1
Abstract
We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system , generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is over the rational function field , and is based upon four natural axioms from algebraic geometry. We prove that the four axioms yield a unique series with meromorphic continuation to the largest possible domain and the desired infinite group of symmetries.
Cite
@article{arxiv.1408.0937,
title = {Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$},
author = {Ian Whitehead},
journal= {arXiv preprint arXiv:1408.0937},
year = {2019}
}
Comments
28 pages. Comments more than welcome. This is the first of three papers based on the author's thesis: http://arxiv.org/abs/1406.0573