14-18 October 2019
University of Lille
Europe/Paris timezone

Square root p-adic L-functions

17 Oct 2019, 09:30
1h
Salle de réunion (University of Lille)

Salle de réunion

University of Lille

Cité Scientifique – Bâtiment M2 59655 Villeneuve d'Ascq Cedex France

Speaker

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 $L(1/2,\mathrm{BC}(\pi)\times\mathrm{BC}(\pi'))$, where $\pi$ and $\pi'$ are cohomological automorphic representations of unitary groups $U(V)$ and $U(V')$, respectively. Here $V$ and $V'$ are hermitian spaces over a CM field, $V$ of dimension $n$, $V'$ of codimension $1$ in $V$, and $\mathrm{BC}$ denotes the twisted base change to $\mathrm{GL}(n) \times \mathrm{GL}(n-1)$.

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