Hypergeometric function and Modular Curvature I. --Hypergeometric functions in Heat Coefficients
Abstract
We give a new proof of the rearrangement lemma that works for all dimensions and all heat coefficients in the study of modular geometry on noncommutative tori. The building blocks of the spectral functions are landed in a hypergeometric family knowns as Lauricella functions of type . We investigate the differential and recursive relations among the family and obtain a full reduction to Gauss hypergeometric functions. As for applications, we give phase one demonstration on how the hypergeometric features lead to new simplifications in computations involved in the modular geometry.
Cite
@article{arxiv.1810.09939,
title = {Hypergeometric function and Modular Curvature I. --Hypergeometric functions in Heat Coefficients},
author = {Yang Liu},
journal= {arXiv preprint arXiv:1810.09939},
year = {2020}
}
Comments
Base on serval new results, I decided to rewrite and split my previous post arXiv:1711.01664 into two parts for publication. Here is the first of the sequel; Major modifications have been made compare to the previous version. arXiv admin note: text overlap with arXiv:1711.01664