Arithmetic of some modular functions = 모듈러 함수의 산술성

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 $N(j_{1,N})$.
Advisors
Koo, Ja-Kyungresearcher구자경researcher
Publisher
한국과학기술원
Issue Date
1999
Identifier
156125/325007 / 000945117
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학과, 1999, [ ii, [75] p. ]

Keywords

Class field; Finite simple group; 모듈러 함수; 유체; Modular function; 유한 단순군

URI
http://hdl.handle.net/10203/41813
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=156125&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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