Modular Invariant of Quantum Tori II: The Golden Mean

TL;DR

This paper computes a specific modular invariant for the quantum torus associated with the golden mean, providing an explicit formula involving Rogers-Ramanujan functions, advancing understanding of quantum tori invariants.

Contribution

It introduces an explicit formula for the modular invariant of the golden mean quantum torus using weighted Rogers-Ramanujan functions, building on prior definitions.

Findings

Modular invariant approximately 9538.25 for the golden mean quantum torus

Explicit formula involving weighted Rogers-Ramanujan functions

Advances understanding of quantum tori invariants

Abstract

In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined. In this paper, we consider the case of the quantum torus associated to the golden mean. We show that the modular invariant is approximately 9538.249655644 by producing an explicit formula for it involving weighted versions of the Rogers-Ramanujan functions.