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Title: A Tannakian Category and a Horizontal Equidistribution Conjecture for Exponential Sums
Authors: Sawin, Will
Advisors: Katz, Nicholas M
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2016
Publisher: Princeton, NJ : Princeton University
Abstract: We construct a Tannakian category of perverse sheaves on the additive group over the integers, with sheaf convolution as the tensor operation. A class of number-theoretic equidistribution problems, including the equidistribution of Gauss sums and Kloosterman sums and the equidistribution of roots of polynomial congruences, can be viewed as problems about the equidistribution of conjugacy classes in the Tannakian group of this category. Using this correspondence, we conjecture answers to these equidistribution questions.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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