ON A MODULAR EQUATION OF DEGREE 23

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 79

Volume : 19 , Issue : 3
DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.6
Author :
K. R. Vasuki (Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570006, Karnataka, INDIA)
Shibu Andia (Department of Mathematics, Vidyavardhaka College of Engineering, Mysuru - 570002, Karnataka, INDIA)

Abstract

On page 249 of his second notebook, Ramanujan incorrectly recorded and crossed out a modular equation of degree 23. B. C. Berndt has corrected and proved the same using the theory of modular forms. The main objective of this article is to prove the modular equation of degree 23 corrected by Berndt by employing the method of parametrization. Using a similar technique, we also prove a modular equation of degree 11 due to Ramanujan.

Keywords and Phrases

Modular equations, hypergeometric series.

A.M.S. subject classification

11F20, 33C75.

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