Functional determinants on spheres and sectors
J.S.Dowker
TL;DR
This paper computes scalar functional determinants on sectors of a 2D disc and spherical caps for arbitrary angles, providing explicit formulas and comparisons with existing results.
Contribution
It offers new explicit formulas for functional determinants on spherical sectors and caps, extending previous work to arbitrary angles and low-dimensional cases.
Findings
Explicit formulas for determinants on sectors and caps
Comparison with existing literature confirms accuracy
Results applicable to conformal Laplacian in low dimensions
Abstract
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of ). The wholesphere and hemisphere expressions are also given, in low dimensions, for both the ordinary and the conformal Laplacian. Comparisons are made with other work.
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