Analytic Number Theory for 0-Cycles /
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| Author / Creator: | Chen, Weiyan, author. |
|---|---|
| Imprint: | 2017. Ann Arbor : ProQuest Dissertations & Theses, 2017 |
| Description: | 1 electronic resource (47 pages) |
| Language: | English |
| Format: | E-Resource Dissertations |
| Local Note: | School code: 0330 |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11715037 |
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| 100 | 1 | |a Chen, Weiyan, |e author. |0 http://id.loc.gov/authorities/names/n80161224 |1 http://viaf.org/viaf/33310905 | |
| 245 | 1 | 0 | |a Analytic Number Theory for 0-Cycles / |c Weiyan Chen. |
| 260 | |c 2017. | ||
| 264 | 1 | |a Ann Arbor : |b ProQuest Dissertations & Theses, |c 2017 | |
| 300 | |a 1 electronic resource (47 pages) | ||
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| 500 | |a Advisors: Benson Farb Committee members: Matthew Emerton. | ||
| 502 | |b Ph.D. |c University of Chicago, Division of the Physical Sciences, Department of Mathematics |d 2017. | ||
| 510 | 4 | |a Dissertation Abstracts International, |c Volume: 78-12(E), Section: B. | |
| 520 | |a 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. | ||
| 546 | |a English | ||
| 590 | |a School code: 0330 | ||
| 690 | |a Mathematics. | ||
| 710 | 2 | |a University of Chicago. |e degree granting institution. |0 http://id.loc.gov/authorities/names/n79058404 |1 http://viaf.org/viaf/143657677 | |
| 720 | 1 | |a Benson Farb |e degree supervisor. | |
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