|
|||||
|
|
Non-linear algebraic differential equations satisfied by a certain family of elliptic functions |
|
| Authors: | Masato Wakayama Keitaro Yamamoto |
| Affiliation: | 1. Institute of Mathematics for Industry, Kyushu University, Motooka Nishi-ku, Fukuoka, 819-0395, Japan 2. Faculty of Mathematics, Kyushu University, Motooka Nishi-ku, Fukuoka, 819-0395, Japan 3. Graduate School of Mathematics, Kyushu University, Hakozaki Higashi-ku, Fukuoka, 812-8581, Japan 4. JASTEC Co., Ltd., 3-5-23, Takanawa, Minato-ku, Tokyo, 108-0074, Japan |
| Abstract: | Kurokawa and Wakayama (Ramanujan J. 10:23–41, 2005) studied a family of elliptic functions defined by certain q-series. This family, in particular, contains the Weierstrass ?-function. In this paper, we prove that elliptic functions in this family satisfy certain non-linear algebraic differential equations whose coefficients are essentially given by rational functions of the first few Eisenstein series of the modular group. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |