Kojima on double Dirichlet series

Subconvexity for a Double Dirichlet Series

For two real characters ψ, ψ of conductor dividing 8 define Z(s,w;ψ, ψ′) := ζ2(2s+ 2w − 1) X d odd L2(s, χdψ)ψ (d) dw where χd = “

Cesàro Summability of Ordinary Double Dirichlet Series

Double Dirichlet Series over Function Fields

We construct a nite-dimensional vector space of functions of two complex variables attached to a smooth algebraic curve C over a nite eld Fq , q odd, and a level. These functions collect the analytic information about the cohomology of the curve and its quadratic twists that is encoded in the corresponding L-functions; they are double Dirichlet series in two independent complex variables s;w. W...

On Kubota’s Dirichlet Series

Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2]. Closely related results are in Eckhardt and Pat...

Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series

The space of toroidal automorphic forms was introduced by Zagier in the 1970s: a GL2-automorphic form is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The interest in this space stems (amongst others) from the fact that an Eisenstein series of weight s is toroidal for a given torus precisely if s is a non-trivial zero of the zeta function of the q...