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SUMMARY:Rationality results for the symmetric and exterior square L-functi
on of GL(2n)
DTSTART;VALUE=DATE-TIME:20170310T090000Z
DTEND;VALUE=DATE-TIME:20170310T100000Z
DTSTAMP;VALUE=DATE-TIME:20201025T061541Z
UID:indico-event-2195@indico.math.cnrs.fr
DESCRIPTION:ERC Advanced Grant : AAMOT (Arithmetic of Automorphic Motives
)\n\nPI : Michael HARRIS\n\n \n\n\nLet $G$ be GL$(2n)$ over a totally re
al number field $F$\, $n\\geq 2$. Let $\\Pi$ be a cuspidal automorphic rep
resentation of $G(\\mathbb A)$\, which is cohomological and a functorial l
ift 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 t
his 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 sy
mmetric square $L$-function at $s=1$ attached to $\\Pi$. As an application
of the latter\, we also obtain a period-free relation between certain quo
tients of twisted symmetric square $L$-functions and a product of Gau\\ss
~sums of Hecke characters.\n \n\nhttps://indico.math.cnrs.fr/event/2195/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2195/
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