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The 2-term Dilogarithm

Cetin Hakimoglu-Brown

Abstract

I derive two non-trivial cubic, two-term dilogarithm identities, inspired by a conjectured cubic two-term dilogarithm identity by Kanade, which I also prove. The identities are believed to be new. I then tie this in with Nahm's equations and r=2 matrices. This is further progress towards classifying all non-trivial 2-term dilogarithm identities with real terms.

The 2-term Dilogarithm

Abstract

I derive two non-trivial cubic, two-term dilogarithm identities, inspired by a conjectured cubic two-term dilogarithm identity by Kanade, which I also prove. The identities are believed to be new. I then tie this in with Nahm's equations and r=2 matrices. This is further progress towards classifying all non-trivial 2-term dilogarithm identities with real terms.
Paper Structure (6 sections, 1 theorem, 27 equations)

This paper contains 6 sections, 1 theorem, 27 equations.

Table of Contents

  1. Introduction
  2. Proof of conjectured 2-term identity
  3. Conjectured 2-term identities
  4. Relation to Nahm's equations
  5. New 2x2 matrices
  6. Concluding remarks

Key Result

Theorem 1

The below identities hold to at least 100 digits: where $j=\frac{1}{2} \sec(2\pi/9)$.

Theorems & Definitions (2)

  • Theorem 1
  • proof