2018/11/19 by Yang Liu, Liu, Yang
Mathematics · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Mathematics and Applications #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1811.07967
openalex publication_date 2018/11/19 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28
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.