Arithmetic of some modular functions모듈러 함수의 산술성

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dc.contributor.advisorKoo, Ja-Kyung-
dc.contributor.advisor구자경-
dc.contributor.authorKim, Chang-Heon-
dc.contributor.author김창헌-
dc.date.accessioned2011-12-14T04:38:54Z-
dc.date.available2011-12-14T04:38:54Z-
dc.date.issued1999-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=156125&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41813-
dc.description학위논문(박사) - 한국과학기술원 : 수학과, 1999, [ ii, [75] p. ]-
dc.description.abstractIn 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.languageeng-
dc.publisher한국과학기술원-
dc.subjectClass field-
dc.subjectFinite simple group-
dc.subject모듈러 함수-
dc.subject유체-
dc.subjectModular function-
dc.subject유한 단순군-
dc.titleArithmetic of some modular functions-
dc.title.alternative모듈러 함수의 산술성-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN156125/325007-
dc.description.department한국과학기술원 : 수학과, -
dc.identifier.uid000945117-
dc.contributor.localauthorKoo, Ja-Kyung-
dc.contributor.localauthor구자경-
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MA-Theses_Ph.D.(박사논문)
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