## Taiwanese Journal of Mathematics

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

### Proof of a Conjecture of Farkas and Kra

#### 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., Volume 23, Number 6 (2019), 1317-1326.

**Dates**

Received: 3 January 2019

Revised: 23 January 2019

Accepted: 10 March 2019

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

**Mathematical Reviews number (MathSciNet)**

MR4033547

**Zentralblatt MATH identifier**

07142975

**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. 23 (2019), no. 6, 1317--1326. doi:10.11650/tjm/190301. https://projecteuclid.org/euclid.twjm/1552442420