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Counting rational points of hyperelliptic curves over finite fields : 초타원 곡선들의 유한체 위의 유리점들의 개수
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Atanas Iliev | - |
dc.contributor.author | 정길용 | - |
dc.date.accessioned | 2017-07-19T09:00:45Z | - |
dc.date.available | 2017-07-19T09:00:45Z | - |
dc.date.issued | 2015-08 | - |
dc.identifier.other | 000000028726 | - |
dc.identifier.uri | https://hdl.handle.net/10371/131498 | - |
dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. Atanas Iliev. | - |
dc.description.abstract | Given a finite field F_q with a prime power q, one can ask how many points an hyperelliptic curve of a large fixed "degree" d > 0 has. It is difficult to answer this question in general, so we can consider a probabilistic answer instead. Such an answer was previously obtained by Kurlberg and Rudnick, precisely when d goes to infinity. This was first generalized by Bucur, David, Feigon, and Lalin for p-fold cyclic covers of the line and later by Cheong, Wood, and Zaman. The two generalizations are different from each other because the limits are taken differently. A main goal of the thesis is a heuristic attempt to give a generalization of these two as a conjecture and solve more cases of it. | - |
dc.description.tableofcontents | Abstract
1. Introduction 2. Objects of main interest 2.1. Notations and facts 2.2. Main discussion 3. Generalizations 3.1. For m = 2, Conjecture 3.3 implies Conjecture 3.4 4. Review: Proof of Theorem 3.2 4.1. Lemmas and Notations 4.2. Proof of Theorem 3.2 5. Main result: Special cases of Conjectures 3.3 and 3.4 5.1. Key ingredients 5.2. Proof of Theorem 5.1 References 국문초록 | - |
dc.format | application/pdf | - |
dc.format.extent | 3170585 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | finite fields | - |
dc.subject | rational points | - |
dc.subject | hyperelliptic curves | - |
dc.subject | zeta functions | - |
dc.subject.ddc | 510 | - |
dc.title | Counting rational points of hyperelliptic curves over finite fields | - |
dc.title.alternative | 초타원 곡선들의 유한체 위의 유리점들의 개수 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | GilYoung Cheong | - |
dc.description.degree | Master | - |
dc.citation.pages | 25 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2015-08 | - |
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