Multiple sine, multiple elliptic gamma functions and rational cones

2014/12/19 by Luigi Tizzano, Tizzano, Luigi, Jacob Winding +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1502.05996

openalex publication_date 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in ℝ^r. For r=2,3 we prove that the generalized multiple elliptic gamma functions enjoy a modular property determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko. The generalized multiple sine enjoy a related infinite product representation, generalizing the results of Narukawa for the ordinary multiple sine functions.

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