L-functions of Kloosterman sheaves
报告人：Yichen Qin (École Polytechnique)
时间：2021-12-27 16:00-17:00
地点：Zoom
Abstract: Kloosterman sums are finite field analogues of Bessel functions. They appear as traces of Frobenius on some \ell-adic local systems Kl_{n+1} on G_m, called Kloosterman sheaves. In a recent work, Fresán-Sabbah-Yu have constructed some motives attached to symmetric powers of Kloosterman sheaves Sym^k Kl_{n+1}, and showed that for n=1, their L-functions have meromorphic extensions to the complex plane and satisfy functional equations. For small values of k, these L-functions are given by modular forms that one can explicitly write down. In this talk, I will present some new results about the L-functions of Sym^k Kl_3. In particular, I will specify some modular forms and explain why these motives are modular in these cases.
Zoom Inforamtion
https://zoom.us/j/89928606536?pwd=VkFLWVIwbis1Q2pzOXR2UlFMZC9LZz09
ID：899 2860 6536
PW：984423
