# Geometric deduction of the solutions to modular equations

@inproceedings{Alam2021GeometricDO, title={Geometric deduction of the solutions to modular equations}, author={Md. Shafiul Alam and Toshiyuki Sugawa}, year={2021} }

In his notebooks, Ramanujan presented without proof many remarkable formulae for the solutions to generalized modular equations. Much later, proofs of the formulae were provided by making use of highly nontrivial identities for theta series and hypergeometric functions. We offer a geometric approach to the proof of those formulae. We emphasize that our proofs are geometric and independent of such identities.

## One Citation

On Ramanujan's Modular Equations and Hecke Groups

- Mathematics
- 2021

We study the relation between Hecke groups and the modular equations in Ramanujan’s theories of signature 2, 3 and 4. The solution (α, β) to the generalized modular equation satisfies a polynomial…

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