Some New Ramanujan's Modular Equations of Degree 15

TL;DR

This paper discovers new modular equations related to Ramanujan's work, specifically involving degrees 3, 5, and 15, and provides concise proofs using Ramanujan's multiplier function.

Contribution

It introduces novel Ramanujan modular equations of degrees 3, 5, and 15, expanding the known set of such equations and employing a new proof technique.

Findings

New modular equations of degrees (3,5) and (1,15)

Concise proofs using Ramanujan's multiplier function

Extension of Ramanujan's original modular equations

Abstract

Ramanujan in his notebook recorded two modular equations involving multiplier with moduli of degrees (1,7) and (1,23). In this paper, we find some new Ramanujan's modular equations involving multiplier with moduli of degrees (3,5) and (1,15), and give concise proofs by employing Ramanujan's multiplier function equation.