Differential and Functional Identities for the Elliptic Trilogarithm

Strachan, I.A.B. (2009) Differential and Functional Identities for the Elliptic Trilogarithm. Symmetry, Integrability and Geometry: Methods and Applications, 5, 031. (doi: 10.3842/SIGMA.2009.031)

Abstract

When written in terms of (sic)-functions, the classical Frobenius-Stickelberger pseudo-addition formula takes a very simple form. Generalizations of this functional identity are studied, where the functions involved are derivatives (including derivatives with respect to the modular parameter) of the elliptic trilogarithm function introduced by Beilinson and Levin. A differential identity satisfied by this function is also derived. These generalized Frobenius-Stickelberger identities play a fundamental role in the development of elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde equations of associativity, with the simplest case reducing to the above mentioned differential identity.

• Item Type: Articles
• Additional Information: Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions Bonn, GERMANY, JUL 21-25, 2008
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Strachan, Professor Ian
• Authors: Strachan, I.A.B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Symmetry, Integrability and Geometry: Methods and Applications
• ISSN: 1815-0659