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Mean Values of Pólya’s Error Term by Justin Cheigh ’24

Tue, May 14th, 2024
1:00 pm
- 1:50 pm

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Mean Values of Pólya’s Error Term by Justin Cheigh ’24, Tuesday May 14, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Mathematics Thesis

 

Abstract: A character sum S is a sum of the values of a Dirichlet character mod q over some interval. It turns out character sums are related to important questions surrounding L-functions and the least quadratic non-residue. In 1918, Pólya and Vinogradov independently proved S << sqrt(q) log q. One potential method to improve this is via Pólya’s Fourier expansion, which expresses S in terms of a main term and an error term. In this work, we prove a mean value result on the asymptotic behavior of the error term.

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