DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Koo, Ja-Kyung | - |
dc.contributor.advisor | 구자경 | - |
dc.contributor.author | Kim, Chang-Heon | - |
dc.contributor.author | 김창헌 | - |
dc.date.accessioned | 2011-12-14T04:38:54Z | - |
dc.date.available | 2011-12-14T04:38:54Z | - |
dc.date.issued | 1999 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=156125&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41813 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학과, 1999, [ ii, [75] p. ] | - |
dc.description.abstract | In this thesis we mainly focus on two subjects: The first is the generation of class fields over an imaginary quadratic fields by special values of modular function with the monster simple group. Based on Hilbert``s 12th problem, that is, the construction of class fields by transcendental method, we will find the modular function $j_{1,8}$ which gives rise to a field generator of function field over the modular curve $X_1(8)$ of genus 0, and with this function we will generate various class fields over an imaginary quadratic field. On the other hand, the "moonshine conjecture" was proposed by Conway-Norton in 1979 and solved by Borcherds in 1992, which suggests a mysterious relationship of modular functions with finite simple groups and infinite dimensional Lie algebras. As a first step to find out this connection, we will derive recursion formulas satisfied by the Fourier coefficients of the normalized generator $N(j_{1,N})$. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Class field | - |
dc.subject | Finite simple group | - |
dc.subject | 모듈러 함수 | - |
dc.subject | 유체 | - |
dc.subject | Modular function | - |
dc.subject | 유한 단순군 | - |
dc.title | Arithmetic of some modular functions | - |
dc.title.alternative | 모듈러 함수의 산술성 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 156125/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000945117 | - |
dc.contributor.localauthor | Koo, Ja-Kyung | - |
dc.contributor.localauthor | 구자경 | - |
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