Riemann's Zeta Function. Numerical Evaluation via its Alternating Relative \eta(s)

TL;DR

This paper presents a method for numerically evaluating Riemann's Zeta function within the critical strip using the alternating eta function, enabling accurate calculations with basic calculators.

Contribution

It introduces a practical approach to compute the Zeta function via the alternating eta function, simplifying calculations within the critical strip.

Findings

Accurate evaluation of ζ(s) within the critical strip.

Method requires only basic scientific calculator.

Discusses accuracy limits of the approach.

Abstract

The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta function {\zeta}(s) is easily obtained from {\eta}(s). The obtained accuracy, within certain limits of the described method is discussed. A decent scientific calculator suffices to carry out the involved computations.