On Weierstrass $\wp$ in signature 3

TL;DR

This paper investigates the relationship between two elliptic functions in signature three, specifically relating their coperiodic Weierstrass  functions, contributing to the understanding of elliptic functions in this signature.

Contribution

It precisely determines the relationship between two elliptic functions constructed by Shen in signature three, focusing on their Weierstrass  functions.

Findings

Established the exact relationship between the two elliptic functions

Connected their coperiodic Weierstrass  functions

Enhanced understanding of elliptic functions in signature three

Abstract

In his work on the Ramanujan theory of elliptic functions to alternative bases, Shen constructed two different elliptic functions in signature three; we determine the precise relationship between them, by precisely relating their coperiodic Weierstrass $\wp$ functions.