| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 6419696 | Advances in Applied Mathematics | 2011 | 17 Pages |
Abstract
We generalize two identities involving Eisenstein series given in Chapter 19 of Ramanujanʼs second notebook. Four infinite families of Eisenstein series are obtained and their properties are investigated. The generating function of each infinite family is shown to be an elliptic function which has a simple infinite product expansion. Transformation properties of the Eisenstein series are investigated from first principles without using the transformation properties of Dedekindʼs eta-function.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Shaun Cooper, Heung Yeung Lam,