Number Theory Seminar
Wednesday, September 28, 2022, 3:15pm, Physics 119
Edna Jones (Duke University)
The Kloosterman circle method and weighted representation numbers of positive definite quadratic forms
Abstract:
We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of positive definite integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, SaliƩ sums, and a principle of nonstationary phase. If time permits, we may discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings. [video]

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