Multiplicative $\eta$-quotients
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- by Yves Martin
- Trans. Amer. Math. Soc. 348 (1996), 4825-4856
- DOI: https://doi.org/10.1090/S0002-9947-96-01743-6
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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.References
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Bibliographic Information
- Yves Martin
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: ymartin@math.berkeley.edu
- Received by editor(s): November 22, 1994
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 4825-4856
- MSC (1991): Primary 11F20; Secondary 11F22
- DOI: https://doi.org/10.1090/S0002-9947-96-01743-6
- MathSciNet review: 1376550