Proof of a conjecture of Farkas and Kra

Nian Hong Zhou

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arXiv · 1812.09901

Proof of a conjecture of Farkas and Kra

Nian Hong Zhou

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Abstract

In this paper we prove a conjectured modular equation of Farkas and Kra, which involving a half sum of certain modular form of weight $1$ for congruence subgroup $\Gamma_1(k)$ with any prime $k$. We prove that their conjectured identity holds for all odd integer $k\ge 2$. A new modular equation of Farkas and Kra type is also established.

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Nian Hong Zhou. 2018-12-24. Proof of a conjecture of Farkas and Kra. https://arxiv.org/abs/1812.09901

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