English

Geometric deduction of the solutions to modular equations

Complex Variables 2021-05-13 v1

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.

Keywords

Cite

@article{arxiv.2105.05759,
  title  = {Geometric deduction of the solutions to modular equations},
  author = {Md. Shafiul Alam and Toshiyuki Sugawa},
  journal= {arXiv preprint arXiv:2105.05759},
  year   = {2021}
}
R2 v1 2026-06-24T02:02:42.030Z