A note on modular equations of signature 2 and their evaluations
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 31-43
Published online July 5, 2021
Printed January 31, 2022
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 : 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
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