Mathematical Sciences Research Institute

Home » Workshop » Schedules » $\ell$-adic trace functions in analytic number theory

$\ell$-adic trace functions in analytic number theory

Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017

February 09, 2017 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Philippe Michel (École Polytechnique Fédérale de Lausanne (EPFL))
Location: MSRI: Simons Auditorium
  • Kloosterman sheaves

  • Kloosterman sums

  • monodromy

  • moments of L-functions

  • arithmetic functions in arithmetic progressions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC

$\Ell$-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.

27977?type=thumb Michel Notes 1.98 MB application/pdf Download
Video/Audio Files

$\Ell$-Adic Trace Functions In Analytic Number Theory

H.264 Video 15-Michel_a.mp4 155 MB video/mp4 rtsp://videos.msri.org/data/000/027/847/original/15-Michel_a.mp4 Download
H.264 Video 15-Michel_b.mp4 479 MB video/mp4 rtsp://videos.msri.org/data/000/027/848/original/15-Michel_b.mp4 Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath Videos page.