Non-linear algebraic differential equations satisfied by a certain family of elliptic functions

作者：Wakayama Masato^*; Yamamoto Keitaro

来源：Ramanujan Journal, 2013, 30(2): 173-186.

DOI：10.1007/s11139-012-9425-3

• Elliptic functions
• q-series
• Weierstrass P-function
• Eisenstein series
• Lambert series

Kurokawa andWakayama (Ramanujan J. 10:23-41, 2005) studied a family of elliptic functions defined by certain q-series. This family, in particular, contains the Weierstrass P-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.

• 出版日期2013-2