TL;DR
This paper introduces a new method for calculating functional determinants based on resolvent asymptotics, applied to Moebius corners with implicit eigenvalues, and extends Barnes' multiple gamma functions.
Contribution
It presents a novel approach to functional determinants using resolvent asymptotics and generalizes Barnes' multiple gamma functions for complex geometries.
Findings
Method effectively computes determinants for Moebius corners.
Generalization of Barnes' product form enhances mathematical tools.
Applicable to cases with implicitly known eigenvalues.
Abstract
A general method of finding functional determinants is presented that depends on the asymptotic behaviour of the resolvent. Its application to the case of a bounded trihedral corner for which the eigenvalues are known only implicitly is outlined and a generalisation of Barnes' product form of multiple gamma functions is given
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