Lower bounds for high moments of zeta sums

TL;DR

This paper establishes unconditional lower bounds for high moments of zeta sums, specifically sums of the form n^{i t}, advancing understanding of their magnitude.

Contribution

It provides the first unconditional lower bounds for high moments of zeta sums, a significant step in analytic number theory.

Findings

Unconditional lower bounds for high moments of zeta sums are proven.

Results contribute to understanding the size and behavior of zeta sums.

The work advances theoretical knowledge in the distribution of zeta sums.

Abstract

In this article, we investigate high moments of zeta sums $\sum_{n\le x}n^{i t}$. We show unconditional lower bounds for them.