Optimization of the Implicit Constant for Upper Bounds for Moments of the Riemann zeta Function

TL;DR

This paper refines and computes explicit constants for upper bounds on moments of the Riemann zeta function, improving previous results by Harper and Soundararajan under specific conditions.

Contribution

It provides optimized explicit constants for upper bounds on zeta function moments, enhancing the precision of prior theoretical bounds.

Findings

Optimized the implicit constant for Harper's upper bounds.

Computed the implicit constant for Soundararajan's bounds under certain conditions.

Improved the accuracy of moment bounds for the Riemann zeta function.

Abstract

We optimized the implicit constant for the refined upper bounds for moments of the Riemann zeta-function proved by Harper. We also computed the implicit constant for the upper bounds for moments of the Riemann zeta-function proved by Soundararajan under certain conditions.