$\ell$-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 L-functions
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
|
Download |
$\Ell$-Adic Trace Functions In Analytic Number Theory
H.264 Video |
06-Michel.mp4
|
Download |
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.