Proceedings of the Japan Academy, Series A, Mathematical Sciences

Computation of the modular equation

Hideji Ito

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 71, Number 3 (1995), 48-50.

Dates
First available: 19 November 2007

Permanent link to this document
http://projecteuclid.org/euclid.pja/1195510765

Mathematical Reviews number (MathSciNet)
MR1332947

Zentralblatt MATH identifier
0832.11017

Digital Object Identifier
doi:10.3792/pjaa.71.48

Subjects
Primary: 11F03: Modular and automorphic functions

Citation

Ito, Hideji. Computation of the modular equation. Proceedings of the Japan Academy, Series A, Mathematical Sciences 71 (1995), no. 3, 48--50. doi:10.3792/pjaa.71.48. http://projecteuclid.org/euclid.pja/1195510765.


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References

  • [1] T. M. Apostol: Modular Functions and Dirichlet Series in Number Theory. Springer (1976).
  • [2] W. E. H. Berwick : An invariant modular equation of the fifth order. Quart. J. Math., 47, 94-103 (1916).
  • [3] J. H. Conway and S. P. Norton : Monstrous moonshine. Bull. London Math. Soc., 11, 308-339 (1979).
  • [4] 0. Herrmann: Uber die Berechung der Fourier-coefficienten der Funktion j(r). J. Riene Angew. Math., 274, 187-195 (1975).
  • [5] E. Kaltofen and N. Yui: On the modular equation of order 11. Proc. of the 1984 MACSYMA User's Conference, 472-485 (1984).
  • [6] D. H. Lehmer : Properties of the coefficients of the modular invariant /(r). Amer. J. Math., 64, 488-502 (1942).
  • [7] J. Lehner: Divisibility properties of the Fourier coefficients of the modular invariant j(z). Amer. J. Math.,71, 136-148 (1949).
  • [8] J. Lehner: Further congruence properties of the Fourier coefficients of the modular invariant j(r). Amer. J. Math., 71, 373-386 (1949).
  • [9] S. Lang: Elliptic Functions. Addison-Wesley (1973).
  • [10] G. N. Watson: Ramanujans Vermutung uber Zerfallungsanzahlen. J. Riene Angew. Math., 179, 97-128 (1938).