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Séminaire de Mathématique

# Rationality results for the symmetric and exterior square L-function of GL(2n)

## by Prof. Harald GROBNER (Université de Vienne)

vendredi 10 mars 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
 Description ERC Advanced Grant : AAMOT (Arithmetic of Automorphic Motives) PI : Michael HARRIS   Let $G$ be GL$(2n)$ over a totally real number field $F$, $n\geq 2$. Let $\Pi$ be a cuspidal automorphic representation of $G(\mathbb A)$, which is cohomological and a functorial lift from SO$(2n+1)$. The latter condition can be equivalently reformulated that the exterior square $L$-function of $\Pi$ has a pole at $s=1$. In this talk, we present a rationality result for the residue of the exterior square $L$-function at $s=1$ and also for the holomorphic value of the symmetric square $L$-function at $s=1$ attached to $\Pi$. As an application of the latter, we also obtain a period-free relation between certain quotients of twisted symmetric square $L$-functions and a product of Gau\ss ~sums of Hecke characters.   Organisé par Michael Harris Contact Email: cecile@ihes.fr