The B-B-G Transfer Principle for signature four

TL;DR

This paper introduces a transfer principle for signature four elliptic functions, connecting Shen's dn_2 function to the work of Berndt, Bhargava, and Garvan, expanding the understanding of elliptic function transformations.

Contribution

It establishes a new transfer principle linking Shen's elliptic function dn_2 with the signature four transfer principle of Berndt, Bhargava, and Garvan.

Findings

Derived a transfer principle from Shen's dn_2 function

Connected elliptic functions to signature four transformations

Enhanced understanding of elliptic function relationships

Abstract

We show how the elliptic function ${\rm dn}_2$ of Shen leads to the signature four transfer principle of Berndt, Bhargava and Garvan.