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December, 2019 Proof of a Conjecture of Farkas and Kra
Nian Hong Zhou
Taiwanese J. Math. 23(6): 1317-1326 (December, 2019). DOI: 10.11650/tjm/190301

Abstract

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.

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Nian Hong Zhou. "Proof of a Conjecture of Farkas and Kra." Taiwanese J. Math. 23 (6) 1317 - 1326, December, 2019. https://doi.org/10.11650/tjm/190301

Information

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

zbMATH: 07142975
MathSciNet: MR4033547
Digital Object Identifier: 10.11650/tjm/190301

Subjects:
Primary: 11F27
Secondary: 11F12 , 14K25

Keywords: modular equations , theta constants , Theta functions

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 6 • December, 2019
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