A problem of Katz on modular structures of Kloosterman sums

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Event details

Date 01.05.2019
Hour 14:1515:15
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

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