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- Title
Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series.
- Authors
Berndt, Bruce C.; Bialek, Paul R.; Yee, Ae Ja
- Abstract
In their last joint paper, G. H. Hardy and S. Ramanujan established a formula for the power series coefficients of a broad class of nonanalytic modular forms. They then applied their theorem to 1/E6(τ), where E6 is an Eisenstein series. In letters written to Hardy from nursing homes in England, Ramanujan communicated several other examples and further theorems on this subject. These claims have not been heretofore proved in print. Some of the examples do not fall under the purview of Hardy and Ramanujan's theorem or those of later mathematicians. The purpose of this paper is to prove several of the aforementioned results from Ramanujan's letters. To do this, extensions of the theorems of Hardy, Ramanujan, and later authors are needed.
- Subjects
POWER series; EISENSTEIN series; HARDY spaces; MODULAR forms; HARDY, G. H. (Godfrey Harold), 1877-1947; RAMANUJAN, S.; MATHEMATICIANS
- Publication
IMRN: International Mathematics Research Notices, 2002, Vol 2002, Issue 21, p1077
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1155/S1073792802107094