A note on order estimates of the $q$-analogue of the Riemann zeta function

TL;DR

This paper provides initial bounds for the $q$-analogue of the Riemann zeta function on vertical lines, aiding the understanding of its order estimates.

Contribution

It offers the first step in estimating the order of the $q$-analogue of the Riemann zeta function by establishing bounds on vertical lines for fixed $q$.

Findings

Bounds for the $q$-analogue of the Riemann zeta function on vertical lines

Initial estimates for order analysis of the $q$-zeta function

Foundation for further study of the $q$-zeta function's properties

Abstract

At the first step of studying order estimates for the $q$-analogue of the Riemann zeta function, we estimate bounds for it on vertical lines for a fixed parameter $q$.