Automorphic p-adic L-functions and regulators

Square root p-adic L-functions

17 oct. 2019, 09:30

1h

Salle de réunion (University of Lille)

Orateur

Michael Harris (Columbia University)

Description

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products. Although the conjecture is not proved in full generality, there has been considerable progress, especially for L-values of the form $L(1/2,\mathrm{BC}(\pi )\times \mathrm{BC}({\pi }^{\prime }))$, where $\pi$ and ${\pi }^{\prime }$ are cohomological automorphic representations of unitary groups $U(V)$ and $U(V^{\prime })$, respectively. Here $V$ and $V^{\prime }$ are hermitian spaces over a CM field, $V$ of dimension $n$, $V^{\prime }$ of codimension $1$ in $V$, and $\mathrm{BC}$ denotes the twisted base change to $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$.