A consequence of Littlewood's conditional estimates for the Riemann zeta-function

TL;DR

This paper explores the implications of Littlewood's conditional estimates for the Riemann zeta-function under RH, advancing understanding of zero-free regions through an approach inspired by Y. Motohashi.

Contribution

It offers a new estimate related to zero-free regions of the zeta-function assuming RH and Littlewood's estimates, connecting classical and modern methods.

Findings

Derived a new estimate for zero-free regions under RH

Linked Littlewood's estimates with Motohashi's approach

Enhanced understanding of the zeta-function's zeros

Abstract

Assuming the Riemann hypothesis (RH) and using Littlewood's conditional estimates for the Riemann zeta-function, we provide an estimate related to an approach of Y. Motohashi to the zero-free region.