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Number Theory Seminar

Thursday, June 2, 2022
4:00pm to 5:00pm
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Linde Hall 387
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

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].