1999/07/23 by Giovanni Felder, Alexander Varchenko · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.CA #math.QA
paper · pdf · doi:10.1006/aima.2000.1951
published as Adv. Math. 156(2000), 44-76 · 27 pages, LaTeX References added, minor corrections
arxiv created 1999/07/23 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The elliptic gamma function is a generalization of the Euler gamma function and is associated to an elliptic curve. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma function, respectively. The elliptic gamma function appears in Baxter's formula for the free energy of the eight-vertex model and in the hypergeometric solutions of the elliptic qKZB equations. In this paper, the properties of this function are studied. In particular we show that elliptic gamma functions are generalizations of automorphic forms of G=SL(3,Z) x Z3 associated to a non-trivial class in H3(G,Z).