A problem of Katz on modular structures of Kloosterman sums

Event details
Date | 01.05.2019 |
Hour | 14:15 › 15:15 |
Speaker | Ping Xi (Xi'an Jiaotong University) |
Category | Conferences - Seminars |
Around 40 years ago, Katz proposed a problem on modular structures of Kloosterman sums that $\pm S(1,1;p)/\sqrt{p}$ with prime moduli $p$ might coincide with the $p$-th Fourier coeffcient of certain Hecke--Maass cusp form for $GL_2$. In this talk, we will show how to combine a weighted Selberg sieve, $\ell$-adic cohomology and spectral theory of automorphic forms to provide a partial ``negative" answer to this problem in the sense of almost prime moduli.
Practical information
- Informed public
- Free
Organizer
- Philippe Michel
Contact
- Monique Kiener