A Brief Note on the Riemann hypothesis II

TL;DR

This paper explores the Riemann hypothesis by analyzing the Euler's alternating series of the zeta function, proposing a regularized ratio in the functional equation, and providing evidence supporting the hypothesis.

Contribution

It introduces a regularized ratio derived from divergent quantities in the functional equation, offering a new perspective on the Riemann hypothesis.

Findings

Evidence supporting the Riemann hypothesis

Definition of a finite ratio from divergent series

Review of key points in the functional equation

Abstract

We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly review the essential points and we also define a finite ratio in the functional equation from divergent quantities in this note.