Time: 9h00, Friday, September 30, 2016
Location: Room 109, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we reduce them to orbital integrals for endoscopy groups and look at this as the special value of $L$-function at $s=0$. And finally show that it is equal to the special value of motivic $L$-function at $s=0$.
Keywords. Galois representation, Shimura variety, special values of L-function, trace formula, Poisson summation formula