2021/05/12 by Md. Shafiul Alam, Toshiyuki Sugawa, Alam, Md. Shafiul +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2105.05759
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.