Generation of class fields by the modular function $j_{1,12}$

• Autorzy: Kuk Jin Hong , Ja Kyung Koo
• Języki publikacji: EN

Kategorie tematyczne

• 14H55: Riemann surfaces; Weierstrass points; gap sequences
• 11R04: Algebraic numbers; rings of algebraic integers
• 11R37: Class field theory
• 11F11: Holomorphic modular forms of integral weight

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 3
• Strony: 257-291

Daty

wydano

2000

otrzymano

1998-11-10

poprawiono

1999-12-16

Twórcy

autor

Kuk Jin Hong

• Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea

autor

Ja Kyung Koo

• Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea

Bibliografia

• [1] I. Chen and N. Yui, Singular values of Thompson series, in: Groups, Difference Sets and the Monster, K. T. Arasu et al. (eds.), de Gruyter, 1996, 255-326.
• [2] J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11 (1979), 308-339.
• [3] D. A. Cox, Primes of the Form x² + ny², Wiley, 1989.
• [4] K. Harada, Moonshine of Finite Groups, lecture note, Ohio State Univ.
• [5] C. H. Kim and J. K. Koo, Arithmetic of the modular function j₄, J. Korean Math. Soc. 36 (1999), 707-724.
• [6] C. H. Kim and J. K. Koo, Arithmetic of the modular function $j_{1,4}$, Acta Arith. 84 (1998), 129-143.
• [7] C. H. Kim and J. K. Koo, Arithmetic of the modular function $j_{1,8}$, Ramanujan J., to appear.
• [8] C. H. Kim and J. K. Koo, Arithmetic of the modular functions $j_{1,5}$ and $j_{1,6}$, in preparation.
• [9] C. H. Kim and J. K. Koo, Arithmetic of the modular functions $j_{1,2}$ and $j_{1,3}$, in preparation.
• [10] C. H. Kim and J. K. Koo, Generation of Hauptmoduln of Γ₁(7), Γ₁(9) and Γ₁(10), in preparation.
• [11] C. H. Kim and J. K. Koo, On the Hauptmodul of Γ₁(12), preprint.
• [12] C. H. Kim and J. K. Koo, On the genus of some modular curve of level N, Bull. Austral. Math. Soc. 54 (1996), 291-297.
• [13] C. H. Kim and J. K. Koo, The normalizer of Γ₁(N) in PSL₂(ℝ), Comm. Algebra, to appear.
• [14] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, 1984.
• [15] S. Lang, Algebraic Number Theory, Springer, 1994.
• [16] S. Lang, Elliptic Functions, Springer, 1987.
• [17] R. Rankin, Modular Forms and Functions, Cambridge Univ. Press, Cambridge, 1977.
• [18] B. Schoeneberg, Elliptic Modular Functions, Springer, 1973.
• [19] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Princeton, 1971.
• [20] G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481.
• [21] J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994.