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Toric modular forms of higher weight

Lev A. Borisov·Paul E. Gunnells
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Abstract

In two previous papers we used the geometry of complete polyhedral fans to construct a subring $\TTT (l)$ of the modular forms on $Γ_{1} (l)$, and showed that for weight two the cuspidal part of $\TTT (l)$ coincides with the space of cusp forms of analytic rank zero. In this paper we show that in weights greater than two, the cuspidal part of $\TTT (l)$ coincides with the space of all cusp forms.

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Lev A. Borisov, Paul E. Gunnells. 2002-03-22. Toric modular forms of higher weight. https://arxiv.org/abs/math/0203242

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