Applications of Ramanujan's work on Eisenstein series

Masato Kobayashi

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arXiv · 2304.13978

Applications of Ramanujan's work on Eisenstein series

Masato Kobayashi

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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).

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Masato Kobayashi. 2023-04-27. Applications of Ramanujan's work on Eisenstein series. https://arxiv.org/abs/2304.13978

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