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Trace functions over finite fields

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In joint works with É. Fouvry and Ph. Michel, we have begun the study of the analytic properties of “trace functions” over finite fields, which are special functions arising from algebraic objects. The talk will explain and motivate this notion, and discuss the results we have obtained (which include sums over primes of trace functions, twists of modular forms by trace functions and estimates for their uniformity norms) as well as some natural remaining analytic questions. The Riemann Hypothesis over finite fields, in its most general form due to Deligne, will play a crucial role.

This talk is part of the Discrete Analysis Seminar series.

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