On quintic Eisenstein series and points of order five of the Weierstrass elliptic functions

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

4-27-2012

Abstract

We employ a new constructive approach to study modular forms of level five by evaluating the Weierstrass elliptic functions at points of order five on the period parallelogram. A significant tool in our analysis is a nonlinear system of coupled differential equations analogous to Ramanujan’s differential system for the Eisenstein series on SL(2,ℤ). The resulting relations of level five may be written as a coupled system of differential equations for quintic Eisenstein series. Some interesting combinatorial and analytic consequences result, including an alternative proof of a famous identity of Ramanujan involving the Rogers–Ramanujan continued fraction.

Comments

Copyright © 2012, Springer Science Business Media, LLC

Recommended Citation

Huber, T. On quintic Eisenstein series and points of order five of the Weierstrass elliptic functions. Ramanujan J 28, 273–308 (2012). https://doi.org/10.1007/s11139-011-9368-0

Publication Title

Ramanujan J

DOI

10.1007/s11139-011-9368-0