Series acceleration formulas are obtained for Dirichlet series with periodic coefficients. Special cases include Ramanujan’s formula for the values of the Riemann zeta function at the odd positive integers exceeding two, and related formulas for values of Dirichlet L-series and the Lerch zeta function.

Recent results on Dirichlet series ∑ n an 1 ns , s ∈ C, with coefficients an in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a classical non-trivial fact due to Bohnenblust and Hille shows that if X is one dimensional, this maximal width heavily depends o...

We prove that a certain vector valued double Dirichlet series satisfying appropriate functional equations is a Mellin transform of a vector valued metaplectic Eisenstein series. We establish an analogous result for scalar double Dirichlet series of the type studied by Siegel.

We develop the theory of “Weyl group multiple Dirichlet series” for root systems of type C. For a root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and functional equations isomorphic to the associated Weyl group. They conjecturally arise as Whittaker coefficients of Eisenstein series on a metaplectic group with cover de...