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Extremal Determinants of Laplace-Beltrami Operators for Rectangular Tori

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arxiv 1709.06006 v3 pith:EYV475YV submitted 2017-09-18 math.NT math.CA

Markus Faulhuber This is my paper · ORCID
classification math.NTmath.CA
keywords torideterminantextremallaplace-beltramirectangularareaargumentsclass
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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.

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  1. On a lattice generalisation of the logarithm and a deformation of the Dedekind eta function

    math.OC 2019-08 conditional novelty 6.0 of 10

    For any dimension in which the lattice theta function has a unique minimizer, that same lattice (pair) uniquely maximizes Gannon's deformed eta function.

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