Abstract
We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac–Moody root system $\widetilde{A}_{n}$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is over the rational function field $\mathbb{F}_{q}(t)$, 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.
Subject
Algebra and Number Theory
Reference17 articles.
1. Multiple Dirichlet Series and Moments of Zeta and L-Functions
2. On some applications of automorphic forms to number theory
3. [DP] A. Diaconu and V. Pasol , Moduli of hyperelliptic curves and multiple Dirichlet series, Preprint.
4. [Pat14] M. Patnaik , Unramified Whittaker functions on p-adic loop groups, Preprint (2014),arXiv:1407.8072 [math.RT].
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献