Hypergeometric function and Modular Curvature I. --Hypergeometric functions in Heat Coefficients
Year: 2018
Type: preprint
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 $D$. 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.
Source: arXiv (Cornell University)
Author: Liu, Yang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2896901613