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2000 | 93 | 3 | 257-291
Tytuł artykułu

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

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