Multiplicative anomaly and zeta factorization

TL;DR

This paper investigates the multiplicative anomaly in zeta determinants, exploring zeta function factorization and its relation to the anomaly, offering new insights by focusing on zeta functions rather than determinants directly.

Contribution

It introduces a simple approach to analyze the multiplicative anomaly and examines zeta function factorization, expanding understanding beyond pseudodifferential operators.

Findings

Zeta function factorization relates to the multiplicative anomaly.

Focus on zeta functions offers new perspectives.

Discussion includes determinants outside pseudodifferential framework.

Abstract

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the multiplicative anomaly issue is discussed. We look primordially into the zeta functions instead of the determinants themselves, as was done in previous work. That provides a supplementary view, regarding the appearance of the multiplicative anomaly. Finally, we briefly discuss determinants of zeta functions that are not in the pseudodifferential operator framework.