A note on modular equations of signature 2 and their evaluations

Belakavadi Radhakrishna Srivatsa Kumar; Arjun Kumar Rathie; Nagara Vinayaka Udupa Sayinath; Shruthi

doi:10.4134/CKMS.c200459

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(1): 31-43

Online first article July 5, 2021 Printed January 31, 2022

https://doi.org/10.4134/CKMS.c200459

A note on modular equations of signature 2 and their evaluations

Belakavadi Radhakrishna Srivatsa Kumar, Arjun Kumar Rathie, Nagara Vinayaka Udupa Sayinath, Shruthi

Manipal Institute of Technology; Rajasthan Technical University; Manipal Institute of Technology; Manipal Institute of Technology

Abstract

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Abstract

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

Keywords: Modular equations, theta functions

MSC numbers: Primary 11F03, 11F27; Secondary 14H42