Thursday, June 02, 2022
4:00 PM -
5:00 PM
Linde Hall 387
Number Theory Seminar
Series: Number Theory Seminar Series
Applied $\ell$-adic cohomology II: Bilinear sums of Kloosterman sums and applications
Philippe Michel,
EPFL/TAN,
Ecole Polytechnique Fédérale de Lausanne,
In this talk we will discuss further applications of $\ell$-adic cohomology to analytic number theory.
In particular we will see that a certain non-trivial bound for bilinear sums of hyper-Kloosterman sums (below the Polya-Vinogradov range) constitute the final ingredient towards the resolution of a longstanding problem concerning moments for twists of $GL_2$ $L$-functions. In turn, these results shed some light on some recent conjectures of Mazur-Rubin regarding the distribution of modular symbols.
These are joint works with V. Blomer, E. Fouvry, E. Kowalski, D. Milicevic and W. Sawin
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For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].