Modular Relations Involving Eisenstein Series

Print ISSN: 0972-7752 | Online ISSN: | Total Downloads : 76

Volume : 11 , Issue : 1
DOI:
Author :
M. S. Mahadeva Naika (Bangalore University, Central Collage Campus, Banglore-560001, Karnataka, INDIA)
C. Shivashankar (Bangalore University, Central Collage Campus, Banglore-560001, Karnataka, INDIA)

Abstract

In this paper, we establish several P—Q modular relations for the ratios involving Eisenstein series analogous to those recorded by Ramanujan in his Notebooks. We also introduce a parametrization js ,t for the series involving Eisenstein series and establish several properties of js ,t.  As an application, we evaluate several explicit values for the Eisenstein series.

Keywords and Phrases

Eisenstein series; Modular equations.

A.M.S. subject classification

11M36, 33C05.

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