On superorthogonality

Lillian Pierce (Duke University)

15-Dec-2020, 21:30-22:30 (3 years ago)

Abstract: The Burgess bound is a well-known upper bound for short multiplicative character sums, which implies for example a subconvexity bound for Dirichlet L-functions. Since the 1950's, people have tried to improve the Burgess method. In order to try to improve a method, it makes sense to understand the bigger “proofscape” in which a method fits. The Burgess method didn’t seem to fit well into a bigger proofscape. In this talk we will show that in fact it can be regarded as an application of “superorthogonality.” This perspective links topics from harmonic analysis and number theory, such as Khintchine’s inequality, Walsh-Paley series, square function estimates and decoupling, multi-correlation sums of trace functions, and the Burgess method. We will survey these connections in an accessible way, with a focus on the number theoretic side.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper )


MIT number theory seminar

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Past semesters

Organizers: Edgar Costa*, Siyan Daniel Li-Huerta*, Bjorn Poonen*, David Roe*, Andrew Sutherland*, Robin Zhang*, Wei Zhang*, Shiva Chidambaram*
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