Trace functions and special functions
Introductory Workshop: Analytic Number Theory February 06, 2017  February 10, 2017
Location: SLMath: Eisenbud Auditorium
Trace functions
exponential sums
monodromy
Bessel functions
Kloosterman sums
11N64  Other results on the distribution of values or the characterization of arithmetic functions
34C27  Almost and pseudoalmost periodic solutions to ordinary differential equations
Trace Functions And Special Functions  Due to technical difficulties, we were only able to capture the first 44 minutes of this lecture.
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
Sawin Notes

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