Given a root system Î¦ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums.â€¦ (More)

To each reduced root system Î¦ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations isâ€¦ (More)

Let Î¦ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Î¦ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large,â€¦ (More)

Let K be a function field of odd characteristic, and let Ï€ (resp.,Î·) be a cuspidal automorphic representation of GL2(AK ) (resp.,GL1(AK )). Then we show that a weighted sum of the twists of L (s, Ï€)â€¦ (More)

A basic idea of Dirichlet is to study a collection of interesting quantities {an}nâ‰¥1 by means of its Dirichlet series in a complex variable w: âˆ‘ nâ‰¥1 ann âˆ’w. In this paper we examine this constructionâ€¦ (More)

We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map g 7â†’ R(g) from GL(2,C)Ã—GL(1,C) to End(V âŠ—V ) where V is aâ€¦ (More)

Weyl group multiple Dirichlet series were associated with a root system Î¦ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker,â€¦ (More)

Let F be a number field and Ï€ be an automorphic representation on GLr (AF ). In this paper we consider weighted sums of quadratic twists of the L-function for Ï€ , âˆ‘ d L(s, Ï€, Ï‡d ) a(s, Ï€, d) Nd âˆ’w ,â€¦ (More)

If F is a local field containing the group Î¼n of n-th roots of unity, and if G is a split semisimple simply connected algebraic group, then Matsumoto [27] defined an n-fold covering group of G(F ),â€¦ (More)