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A note on modular equations of signature 2 and their evaluations
Belakavadi Radhakrishna Srivatsa Kumar,Arjun Kumar Rathie,Nagara Vinayaka Udupa Sayinath,SHRUTHI 대한수학회 2022 대한수학회논문집 Vol.37 No.1
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.
On Some Modular Equations in the Spirit of Ramanujan
Srivatsa Kumar, Belakavadi Radhakrishna Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.
Kumar, Belakavadi Radhakrishna Srivatsa,Vidya, Harekala Chandrashekara Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
In the present paper, we establish relationship between continued fraction U(-q) of order 12 and Ramanujan's cubic continued fraction G(-q) and $G(q^n)$ for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(-q) by using two parameters for Ramanujan's theta-functions and their explicit values.