Hypergeometric function and Modular Curvature II. Connes-Moscovici functional relation after Lesch's work

Abstract

As the second part of the sequel, we investigate the variation of rearrangement operators (more precisely, the spectral functions behind) arising in the study of modular geometry on noncommutative (two) tori. We initiate a systematic approach by introducing transformations corresponding to basic operations in calculus, like differentiation and integration by parts. As for applications, we extend, in a uniform way, the Connes-Moscovici's functional relations on noncommutative two tori attached to the variation of second heat coefficients to noncommutative tori of arbitrary dimension. Moreover, those transformations lead to more internal relations among the hypergeometric family obtained in part I of the sequel, which allows us to obtain, the first time, a computer-aid free verification of those Connes-Moscovici type functional relations.

arXiv commentnumerous small updates to the previous version

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• Modular curvature and Morita equivalence
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Cited by in corpus (5)

• Laplace-Beltrami Operators on Noncommutative Tori
• Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results
• Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
• Pseudodifferential calculus on noncommutative tori, II. Main properties
• General Rearrangement Lemma for Heat Trace Asymptotic on Noncommutative Tori