In this paper we consider two Rankin-Selberg integrals which were discovered by David Ginzburg, and announced in [G-H1]. These integrals are defined on a split form of GSO2n (see below for precise definition), and involve a generic cuspidal automorphic representation of this group. We content ourselves with showing that both integrals unfold to Eulerian integrals involving Whittaker functions, ...

Abstract We study the Picard–Lefschetz formula for Siegel modular threefolds of paramodular level and prove weight-monodromy conjecture its middle degree inner cohomology. give some applications to Langlands programme: using Rapoport-Zink uniformisation supersingular locus special fiber, we construct a geometric Jacquet–Langlands correspondence between $${\text {GSp}}_4$$ <mml:math xmlns:mml="h...

This paper gives a Langlands classification of constituents of ramified principal series representations for split p-adic groups with connected center.

Abstract We calculate, in the framework of geometric Langlands program, periods cuspidal automorphic sheaves for $\operatorname{GL}_{2n}$ along Levi subgroup $\operatorname{GL}_n\times \operatorname{GL}_n$. also solve corresponding local problem.

In the late 1960’s, Robert Langlands introduced a number of ideas to the theory of automorphic forms and formulated a number of conjectures which gave the theory a new focus. I was a colleague of his at this time, and a good deal of my professional energy since then has been directed to problems posed by him. Thus it was not entirely inappropriate that when I was invited to this conference, Miy...