Spherical Casimir energies and Dedekind sums

TL;DR

This paper derives explicit formulas for Casimir energies on lens spaces using generalized Dedekind sums, providing a recursive method for their evaluation, which advances understanding of quantum field effects in curved spaces.

Contribution

It introduces a new approach to compute Casimir energies on lens spaces via generalized Dedekind sums and a recursive evaluation method.

Findings

Explicit formulas for Casimir energies on lens spaces.

Evaluation of Dedekind sums as functions of lens space order.

A recursive method for efficient computation.

Abstract

Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used.