CLASS FIELDS FROM THE FUNDAMENTALTHOMPSON SERIES OF LEVEL N = o(g)
CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N = o(g)
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Thompson series is a Hauptmodul for a genus zero group which lies between ¡0(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class ¯elds over an imaginary quadratic ¯eld K from the Thompson series Tg(??) (Theorem 4), which would be an extension of [3], Theorem 3:7:5 (2) by using the Shimura theory and the standard results of complex multiplica- tion. Also we construct various class ¯elds over K, over a CM-¯eld K(³N + ³¡1 N ), and over a ¯eld K(³N). Furthermore, we ¯nd an explicit formula for the conjugates of Tg(??) to calculate its minimal polynomial where ??(2 H) is the quotient of a basis of an integral ideal in K.
Abstract
Thompson series is a Hauptmodul for a genus zero group which lies between ¡0(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class ¯elds over an imaginary quadratic ¯eld K from the Thompson series Tg(??) (Theorem 4), which would be an extension of [3], Theorem 3:7:5 (2) by using the Shimura theory and the standard results of complex multiplica- tion. Also we construct various class ¯elds over K, over a CM-¯eld K(³N + ³¡1 N ), and over a ¯eld K(³N). Furthermore, we ¯nd an explicit formula for the conjugates of Tg(??) to calculate its minimal polynomial where ??(2 H) is the quotient of a basis of an integral ideal in K.
참고문헌 (8)
- "Monstrus moonshine and monstrous Lie superalgebras", 109, pp.405~444 (1992)
- "Seminar on ComplexMultiplicaton Lectrue Notes in Math21" (1966), Springer-Verlag
- "Singular values of Thompson series; Groups, Dierence setsand Monster, eds", pp.255~326 (1995)
- "Monstrous moonshine", 11, pp.308~339 (1979)
- "Note uber das Geschlecht gewisser arithmetischer Gruppen", 205, pp.173~179 (1973)
- "Arithmetic of the modular functionj 1;4, Acta Arith.84", pp.129~143 (1998)
- "Lecture Notes in Math676 University of Michgan"
- "Introduction to the Arithmetic Theory of Automorphic Functions" (1971)