Subconvexity for a 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...

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...

Dirichlet Series

This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...