Geodesic
On Ramanujan's modular equations and Hecke groups
Md. Shafiul Alam1
1University of Barishal, Department of Mathematics, and Tohoku University, Graduate School of Information Sciences
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 461–471

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Inspired by the work of Ramanujan, many people have studied generalized modular equations and the numerous identities found by Ramanujan. These identities known as modular equations can be transformed into polynomial equations. There is no developed theory about how to find the degrees of these polynomial modular equations explicitly. In this paper, we determine the degrees of the polynomial modular equations explicitly and study the relation between Hecke groups and modular equations in Ramanujan's theories of signatures 2, 3, and 4.
DOI : 10.54330/afm.146802
Keywords: Modular equation, hypergeometric function, Hecke group, congruence subgroup

Md. Shafiul Alam  1

1 University of Barishal, Department of Mathematics, and Tohoku University, Graduate School of Information Sciences 
Md. Shafiul Alam. On Ramanujan's modular equations and Hecke groups. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 461–471. doi: 10.54330/afm.146802
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