Analytic Number Theory for 0-Cycles /

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Bibliographic Details
Author / Creator:Chen, Weiyan, author.
Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:1 electronic resource (47 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Benson Farb Committee members: Matthew Emerton.
Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Summary:There is a well-known analogy between positive and polynomials over finite fields, and a vast literature on analytic number theory for polynomials. From a geometric point of view, monic polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to effective 0-cycles on more general varieties? In this thesis, we present several results supporting a positive answer to this question. Inspired by classical and modern results in analytic number theory, we study the "prime factorization" of random effective 0-cycles on varieties, generalizing previous works on polynomials.