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


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)


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.


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