On the p-adic interpolation of Asai L-values

Abstract: One theme of the relative Langlands program is that period integrals of an automorphic representation of $G$ over a subgroup $H$ often detect functorial transfer from some other group $G'$; moreover, such period integrals often compute special L-values. It is natural to expect p-adic L-functions interpolating these period integrals as the automorphic representation varies in p-adic families, which should encode geometric information about the eigenvariety of $G$. In this talk, we consider the Flicker-Rallis periods, for which $G =\mathrm{GL}_n(K)$ and $H = \mathrm{GL}_n(\mathbf Q)$ for an imaginary quadratic field K and outline the construction of a p-adic L-function on the eigenvariety of $G$ interpolating certain non-critical Asai L-values. We discuss the case n=2 in some detail before moving on to general n, which is work in progress with Daniel Barrera Salazar and Chris Williams.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)