Generation of class fields by the modular function j 1 , 12

Kuk Jin Hong; Ja Kyung Koo

Acta Arithmetica (2000)

  • Volume: 93, Issue: 3, page 257-291
  • ISSN: 0065-1036

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Kuk Jin Hong, and Ja Kyung Koo. "Generation of class fields by the modular function $j_{1,12}$." Acta Arithmetica 93.3 (2000): 257-291. <http://eudml.org/doc/207414>.

@article{KukJinHong2000,
author = {Kuk Jin Hong, Ja Kyung Koo},
journal = {Acta Arithmetica},
keywords = {class fields; modular forms; modular curves; Jacobi theta series},
language = {eng},
number = {3},
pages = {257-291},
title = {Generation of class fields by the modular function $j_\{1,12\}$},
url = {http://eudml.org/doc/207414},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Kuk Jin Hong
AU - Ja Kyung Koo
TI - Generation of class fields by the modular function $j_{1,12}$
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 3
SP - 257
EP - 291
LA - eng
KW - class fields; modular forms; modular curves; Jacobi theta series
UR - http://eudml.org/doc/207414
ER -

References

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  1. [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. Zbl0918.11024
  2. [2] J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11 (1979), 308-339. 
  3. [3] D. A. Cox, Primes of the Form x² + ny², Wiley, 1989. 
  4. [4] K. Harada, Moonshine of Finite Groups, lecture note, Ohio State Univ. 
  5. [5] C. H. Kim and J. K. Koo, Arithmetic of the modular function j₄, J. Korean Math. Soc. 36 (1999), 707-724. Zbl0943.11024
  6. [6] C. H. Kim and J. K. Koo, Arithmetic of the modular function j 1 , 4 , Acta Arith. 84 (1998), 129-143. Zbl0907.11014
  7. [7] C. H. Kim and J. K. Koo, Arithmetic of the modular function j 1 , 8 , Ramanujan J., to appear. Zbl1196.11062
  8. [8] C. H. Kim and J. K. Koo, Arithmetic of the modular functions j 1 , 5 and j 1 , 6 , in preparation. Zbl1196.11062
  9. [9] C. H. Kim and J. K. Koo, Arithmetic of the modular functions j 1 , 2 and j 1 , 3 , in preparation. Zbl1196.11062
  10. [10] C. H. Kim and J. K. Koo, Generation of Hauptmoduln of Γ₁(7), Γ₁(9) and Γ₁(10), in preparation. 
  11. [11] C. H. Kim and J. K. Koo, On the Hauptmodul of Γ₁(12), preprint. 
  12. [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. Zbl0894.11018
  13. [13] C. H. Kim and J. K. Koo, The normalizer of Γ₁(N) in PSL₂(ℝ), Comm. Algebra, to appear. 
  14. [14] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, 1984. Zbl0553.10019
  15. [15] S. Lang, Algebraic Number Theory, Springer, 1994. Zbl0811.11001
  16. [16] S. Lang, Elliptic Functions, Springer, 1987. Zbl0615.14018
  17. [17] R. Rankin, Modular Forms and Functions, Cambridge Univ. Press, Cambridge, 1977. Zbl0376.10020
  18. [18] B. Schoeneberg, Elliptic Modular Functions, Springer, 1973. 
  19. [19] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Princeton, 1971. Zbl0221.10029
  20. [20] G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481. Zbl0266.10022
  21. [21] J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994. Zbl0911.14015

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