Proof of a conjecture of Farkas and Kra
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 1(k) with any prime k. We prove that their conjectured identity holds for all odd integer k 2. A new modular equation of Farkas and Kra type is also established.
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