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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory