Extremal Determinants of Laplace-Beltrami Operators for Rectangular Tori
Number Theory
2020-02-21 v3 Classical Analysis and ODEs
Abstract
In this work we study the determinant of the Laplace-Beltrami operator on rectangular tori of unit area. We will see that the square torus gives the extremal determinant within this class of tori. The result is established by studying properties of the Dedekind eta function for special arguments and refined logarithmic convexity and concavity results of the classical Jacobi theta functions of one real variable are deeply involved.
Keywords
Cite
@article{arxiv.1709.06006,
title = {Extremal Determinants of Laplace-Beltrami Operators for Rectangular Tori},
author = {Markus Faulhuber},
journal= {arXiv preprint arXiv:1709.06006},
year = {2020}
}
Comments
In Version 3 a flaw in the proof of Prop. 3.15 is corrected, which was detected during the review process. To appear in "Mathematische Zeitschrift"