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.

As an alternative to the Dirichlet counterterms prescription, I introduce the concept of Kounterterms as the boundary terms with explicit dependence on the extrinsic curvature Kij that regularize the AdS gravity action. Instead of a Dirichlet boundary condition on the metric, a suitable choice of the boundary conditions –compatible with any asymptotically AdS (AAdS) spacetime– ensures a finite ...

By (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pole-type boundary behavior of corresponding Dirichlet series. Under a weak Riemann-type hypothesis, the boundary behavior of weighted sums of the Dirichlet series can be expressed in terms of the behavior of certain double sums Σ 2k(s). The latter involve the complex zeros of ζ(s) and depend in an essentia...

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...