Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

Modular forms from the Weierstrass functions

Pages: 967 – 980

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a2

Authors

Hiroki Aoki (Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)

Kyoji Saito (Research Institute for Mathematical Sciences, Kyoto University, Sakyoku Kitashirakawa, Kyoto, Japan; and Laboratory of AGHA, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russian Federation)

Abstract

We construct holomorphic elliptic modular forms of weight $2$ and weight $1$, by special values of Weierstrass $\wp$-functions, and by differences of special values of Weierstrass $\zeta$-functions, respectively. Also we calculated the values of these forms at some cusps.

Keywords

Weierstrass $\wp$-function, Weierstrass $\zeta$-function, elliptic modular forms, period integral

2010 Mathematics Subject Classification

11F12, 33E05

Received 17 September 2019

Accepted 10 September 2019

Published 13 November 2020