Taiwanese Journal of Mathematics

Proof of a Conjecture of Farkas and Kra

Nian Hong Zhou

Advance publication

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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.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 10 pages.

Dates
First available in Project Euclid: 13 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1552442420

Digital Object Identifier
doi:10.11650/tjm/190301

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

Keywords
theta functions theta constants modular equations

Citation

Zhou, Nian Hong. Proof of a Conjecture of Farkas and Kra. Taiwanese J. Math., advance publication, 13 March 2019. doi:10.11650/tjm/190301. https://projecteuclid.org/euclid.twjm/1552442420


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References

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