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 case of Flicker--Rallis periods, where $G = \mathrm{GL}_n(K)$ 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. This is work in progress with Daniel Barrera Salazar and Chris Williams.

number theory

Audience: researchers in the topic

London number theory seminar

Series comments: For reminders, join the (very low traffic) mailing list at mailman.ic.ac.uk/mailman/listinfo/london-number-theory-seminar

For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html