$\ell$adic trace functions in analytic number theory
Introductory Workshop: Analytic Number Theory February 06, 2017  February 10, 2017
Location: SLMath: Eisenbud Auditorium
Kloosterman sums
Kloosterman sheaves
monodromy
moments of Lfunctions
arithmetic functions in arithmetic progressions
$\Ell$Adic Trace Functions In Analytic Number Theory
Trace functions are arithmetic functions defined modulo $q$ (some prime number) obtained as Frobenius trace function of $\ell$adic sheaves. The basic example is that of a Dirichlet character of modulus $q$ but there are many other examples of interest for instance (hyper)Kloosterman sums. In this series of lectures we will explain how they arise in classical problems of analytic number theory and how (basi) methods from $\ell$adic cohomology allow to extract a lot out of them. Most of these lectures are based on works of E. Fouvry, E. Kowalski, myself and W. Sawin.
Michel Notes

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