Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 11F20, 11F22

Retrieve articles in all journals with MSC (1991): 11F20, 11F22

Additional Information

Yves Martin
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

Received by editor(s): November 22, 1994
Article copyright: © Copyright 1996 American Mathematical Society