New Formulas for the Riemann Zeta Function

TL;DR

This paper introduces a novel method for analytically continuing the Riemann zeta function using a new approach to the Dirichlet series, supported by numerical experiments showing its computational effectiveness.

Contribution

It presents a new formula for the continuation of the Riemann zeta function, enhancing computational methods for this fundamental mathematical object.

Findings

Effective numerical continuation demonstrated

Improved computational efficiency shown

New formulas for zeta function derived

Abstract

A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.