School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Parameterizations for quintic Eisenstein series
Document Type
Article
Publication Date
2013
Abstract
In his Lost Notebook, Ramanujan gave product expansions for a pair of weight two Eisenstein series of level five. We show that Ramanujan’s formulas are special cases of more general parameterizations for quintic Eisenstein series. In particular, we prove that the Eisenstein series for the Hecke subgroup of level five are expressible as homogeneous polynomials in two parameters closely connected with the Rogers–Ramanujan functions. Moreover, the coefficients of each polynomial are symmetric in absolute value about the middle terms. Corresponding polynomial expansions for allied series, including Eisenstein series on the full modular group, are also derived.
Recommended Citation
Charles, R., Huber, T., & Mendoza, A. (2013). Parameterizations for quintic Eisenstein series. Journal of Number Theory, 133(1), 195–214. https://doi.org/10.1016/j.jnt.2012.06.006
Publication Title
Journal of Number Theory
DOI
10.1016/j.jnt.2012.06.006
Comments
© 2012 Elsevier Inc. All rights reserved. Original published version available at http://dx.doi.org/10.1016/j.jnt.2012.06.006