Some singular values of the elliptic lambda function and incredible cubic identities

TL;DR

This paper presents explicit formulas for the elliptic lambda function, derives remarkable cubic identities, and evaluates specific singular values, advancing understanding of elliptic functions and their algebraic properties.

Contribution

It introduces new explicit formulas for the elliptic lambda function and derives notable cubic identities, providing explicit evaluations of singular values.

Findings

Explicit formulas for the elliptic lambda function

Derivation of remarkable cubic identities

Explicit evaluation of certain singular values

Abstract

We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the elliptic lambda function explicitly.