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Graduate Student Number Theory Seminar

The Gauss Circle Problem

Louis Gaudet - Rutgers University

Location:  Hill 425
Date & time: Thursday, 01 November 2018 at 11:00AM - 11:50AM

Abstract: The Gauss circle problem is to determine an asymptotic formula for the number of integer lattice points contained in a circle centered at the origin as the radius tends to infinity. While the main term is easily determined by a geometric argument, the exact order of magnitude of the error is still today an open problem. I will discuss and prove several main results known about the problem: the classical improvement on the error bound, a lower bound on the error, and an explicit formula. These results nicely demonstrate some fundamental analytic techniques in number theory.

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