A technical note on the calculation of GJMS (Rac and Di) operator determinants

TL;DR

This paper presents a method for efficiently computing determinants of GJMS operators in odd dimensions, applicable to scalar and spinor fields, using sums of Dirichlet eta functions with polynomial coefficients.

Contribution

It introduces a novel approach to calculate GJMS operator determinants as sums of Dirichlet eta functions, simplifying the process in odd dimensions for various field types.

Findings

Determinants expressed as sums of Dirichlet eta functions

Applicable to scalar and spinor fields in odd dimensions

Effective in both sub-critical and super-critical cases

Abstract

GJMS operator determinants in odd dimensions are quickly computed for scalar and spinor fields in both sub- and super-critical cases as sums of Dirichlet eta functions with polynomials in the (integer) operator order as coefficients.