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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multiplicative $ \eta $-quotients


Author: Yves Martin
Journal: Trans. Amer. Math. Soc. 348 (1996), 4825-4856
MSC (1991): Primary 11F20; Secondary 11F22
MathSciNet review: 1376550
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Abstract: Let $ \eta (z) $ be the Dedekind $ \eta $-function. In this work we exhibit all modular forms of integral weight $ f(z) = \eta (t_1z)^{r_1}\eta (t_2z)^{r_2}\dots \eta(t_sz)^{r_s} $, for positive integers $ s $ and $ t_j $ and arbitrary integers $ r_j $, such that both $ f(z) $ and its image under the Fricke involution are eigenforms of all Hecke operators. We also relate most of these modular forms with the Conway group $ 2 % \mathrm {Co}_1 $ via a generalized McKay-Thompson series.


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Additional Information

Yves Martin
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: ymartin@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01743-6
PII: S 0002-9947(96)01743-6
Received by editor(s): November 22, 1994
Article copyright: © Copyright 1996 American Mathematical Society