Rational approximations to the zeta function II

TL;DR

This paper presents continued fraction representations for rational approximations to the zeta function, aiming to analyze their properties and potential zero-free regions.

Contribution

It introduces continued fraction representations for recent rational approximations to the zeta function, offering a new approach for their analysis.

Findings

Continued fraction representations for zeta function approximations

Potential analysis of zero-free regions using Worpitzky-type arguments

Foundation for further analytical techniques on zeta approximations

Abstract

This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of the Worpitzky argument so as to produce zero-free regions for the approximations.