Class fields related to the thompson series and certain arithmetic curves = 톰슨 급수와 산술적 곡선에 관련된 유체들

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In this paper, we generate the class fields by special values of modular functions at imaginary quadratic arguments, over imaginary quadratic field K. Thompson series is a Hauptmodul for a genus zero group which lies between $ \Gamma_0(N)$ and its normalizer in $PSL_2(\Bbb R)$ ([2]). We construct explicit ring class fields over an imaginary quadratic field $K$ from the Thompson series $T_g$, which would be an extension of [Theorem 3.7.5 (2)]{Chen} by using the Shimura theory. The function field $K(X_1(N)^*)$ over $X_1(N)^*$ is a rational function field over $\mathbb{C}$ since the modular curve $X_1(N)^* = \Gamma _1(N)\backslash \frak{H}^*$ has genus zero exactly for the fourteen case 1 ≤ N ≤ 12, 14 and N=15. We find such a field generator $j^*_{1,N}$ and construct explicit class fields over an imaginary quadratic field K from the modular function $j^*_{1,N}$ and $\zeta _N+ \Gamma_N^{-1}$ by using the Shimura`s reciprocity.
Advisors
Koo, Ja-Kyungresearcher구자경researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2004
Identifier
237506/325007  / 000975392
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2004.2, [ iii, 62 p. ]

Keywords

MODULAR CURVE; THOMPSON SERIES; CLASS FIELD; 유체; 보형곡선; 톰슨 급수

URI
http://hdl.handle.net/10203/41873
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=237506&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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