# Thesis Defense

Infinite Symmetric Power L-Functions of HyperKloosterman Sums

Martin Snow

Friday, June 12th, 2020

1:00 PM - 3:00 PM

Zoom

1:00 PM - 3:00 PM

Zoom

The family of hyperKloosterman sums can be studied through the k-th symmetric power L-function. These L-functions are p-adically continuous in k, and so we may take limits, producing the infinite symmetric power L-function. This work develops a p-adic cohomology theory and Frobenius structure for these L-functions, similar in nature to classical L-functions, except in this case we do not expect rationality. Instead, we expect H^1 to be infinite dimensional, and prove H^0 is at most of finite dimension or 0. Consequently, these L-functions are p-adic entire.

Event contact: cynthia dot spencer at rochester dot edu

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