Geometric deduction of the solutions to modular equations
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.05759
- arXiv:
- arXiv:2105.05759
- Bibcode:
- 2021arXiv210505759S
- Keywords:
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- Mathematics - Complex Variables;
- Primary 30F35;
- Secondary 33C05;
- 33E05;
- 30F10