Explicit bounds for the Riemann zeta-function on the 1-line

TL;DR

This paper derives explicit bounds for the Riemann zeta-function on the 1-line using advanced analytical methods, providing clearer estimates crucial for understanding its behavior near the critical line.

Contribution

It introduces new explicit bounds on the zeta-function on the 1-line, utilizing high-order van der Corput lemmas and Borel-Carathéodory theorem, advancing previous estimates.

Findings

Explicit bounds for ζ(1+it) established

Methods improve upon previous estimates

Results aid in understanding zeta-function behavior

Abstract

Explicit estimates for the Riemann zeta-function on the $1$-line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Carath\'{e}odory.