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Modular forms and the automorphism group of Leech lattice

Published online by Cambridge University Press:  22 January 2016

Masao Koike
Masao Koike*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
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This is a continuation of my previous papers [2], [3], [4] concerning to the monstrous moonshine.

The automorphism group ·O of the Leech lattice L plays an important role in the study of moonshine. Especially it is important to study theta functions associated with quadratic sublattices of L consisting of fixed vectors of elements of ·O. In this paper, we discuss the properties that these functions are expected to satisfy in the relation to the monstrous moonshine.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 63 - 79
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Conway, J. H. and Norton, S. P., Monstrous moonshine, Bull. London Math. Soc., 11 (1979), 308–339.Google Scholar
[2] Koike, M., On Mckay’s conjecture, Nagoya Math. J., 95 (1984), 85–89.Google Scholar
[3] Koike, M., Mathieu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147–157.CrossRefGoogle Scholar
[4] Koike, M., Moonshines of PSL2(F q) and the automorphism group of Leech lattice, Japan. J. Math., 12 (1986), 283–323.Google Scholar
[5] Kondo, T., The automorphism group of Leech lattice and elliptic modular functions, J. Math. Soc. Japan, 37 (1985), 337–362.CrossRefGoogle Scholar
[6] Kondo, T. and Tasaka, T., The theta functions of sublattices of the Leech lattice, Nagoya Math. J., 101 (1986), 151–179.Google Scholar
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[8] Lang, M., On a question raised by Conway and Norton, preprint.Google Scholar