Zeta-Function Regularization is Uniquely Defined and Well

TL;DR

This paper rigorously proves that Hawking's zeta function regularization is uniquely defined, clarifying misconceptions and errors that have persisted in scientific literature, thereby solidifying its mathematical foundation.

Contribution

It provides a rigorous proof of the uniqueness of Hawking's zeta function regularization, resolving longstanding misconceptions and errors.

Findings

Zeta function regularization is rigorously and uniquely defined.

Clarification and correction of common misconceptions and errors.

Strengthening the mathematical foundation of the regularization method.

Abstract

Hawking's zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method ---and other analytical procedures--- are clarified and corrected.