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On McKay’s conjecture

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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Let η(z) be Dedekind’s η-function. For any set of integer g = (k1 …, Ks), k1 ≥ k2 ≥ … ≥ks ≥ 1, put . In this paper, we shall prove McKay’s conjecture which gives some combinatorial conditions about ki on which ηg(z) is a primitive cusp form. As to McKay’s conjecture, we refer [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 95 , September 1984 , pp. 85 - 89
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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[ 2 ] Hijikata, H., Explicit formula of the traces of Hecke operators for ΓQ(N), J. Math. Soc. Japan, 26 (1974), 56–82.Google Scholar
[ 3 ] Honda, T. and Miyawaki, I., Zeta functions of elliptic curves of 2-power conductor, J. Math. Soc. Japan, 26 (1974), 362–373.Google Scholar
[ 4 ] Mason, G., M24 and certain automorphic forms, preprint.Google Scholar
[ 5 ] Dummit, D., Kisilevsky, H. and McKay, J., Multiplicative products of η-functions, preprint.Google Scholar