This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions. We begin by explaining how such series arise from Rankin-Selberg constructions. Then more recent work, using Hartogs’ continuation principle as extended by Bochner in place of such constructions, is described. Applications to the nonvanishing of Lfunctions and to other probl...

In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by PerrinRiou for Heegner points when the global sign is −1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions, and an improvement of...

— We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s = k of the associated Dirichlet series....

The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article precursor [1...