Applications of Ramanujan's work on Eisenstein series
Number Theory
2023-05-02 v2
Abstract
Ramanujan (1916) expressed quotients of certain q-series as polynomials of Eisenstein series of degree 2, 4, 6 and derived the famous Ramanujan's differential equations. We continue this research with the variants of Eisenstein-type series which Hahn (2007) recently introduced. We also prove new formulas of convolution sums for divisor sum functions as subsequent work of Cheng- Williams (2004) and Huard-Ou-Spearman-Williams (2002).
Keywords
Cite
@article{arxiv.2304.13978,
title = {Applications of Ramanujan's work on Eisenstein series},
author = {Masato Kobayashi},
journal= {arXiv preprint arXiv:2304.13978},
year = {2023}
}
Comments
20 pages. Fixed some typos (May 1, 2023)