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Trace functions and special functions

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

February 10, 2017 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Will Sawin (ETH Z├╝rich)
Location: MSRI: Simons Auditorium
  • Trace functions

  • exponential sums

  • monodromy

  • Bessel functions

  • Kloosterman sums

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


I will explain the analogy between trace functions over finite fields defined by exponential sums and certain classical functions on the complex numbers defined by integrals of exponentials. There are close analogies, largely due to Katz, that sometimes allow one to guess results in one domain from results in the other. For instance, many important properties of Kloosterman sums are related to facts about Bessel functions. I will explain some of these correspondences, and how to use them to understand exponential sums

27978?type=thumb Sawin Notes 2.12 MB application/pdf Download
Video/Audio Files

Trace Functions And Special Functions - Due to technical difficulties, we were only able to capture the first 44 minutes of this lecture.

H.264 Video 16-Sawin_Partial.mp4 498 MB video/mp4 rtsp://videos.msri.org/data/000/027/876/original/16-Sawin_Partial.mp4 Download
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