Taiwanese Journal of Mathematics

Proof of a Conjecture of Farkas and Kra

Nian Hong Zhou

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In this paper we prove a conjecture of Farkas and Kra, which is a modular equation 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 conjecture holds for all odd integers $k \geq 3$. A new modular equation of Farkas and Kra type is also established.

Article information

Taiwanese J. Math., Volume 23, Number 6 (2019), 1317-1326.

Received: 3 January 2019
Revised: 23 January 2019
Accepted: 10 March 2019
First available in Project Euclid: 13 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F27: Theta series; Weil representation; theta correspondences
Secondary: 11F12: Automorphic forms, one variable 14K25: Theta functions [See also 14H42]

theta functions theta constants modular equations


Zhou, Nian Hong. Proof of a Conjecture of Farkas and Kra. Taiwanese J. Math. 23 (2019), no. 6, 1317--1326. doi:10.11650/tjm/190301. https://projecteuclid.org/euclid.twjm/1552442420

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