Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01dz010s47x
 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. URI: http://arks.princeton.edu/ark:/88435/dsp01dz010s47x Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http://catalog.princeton.edu/ Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

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