Mixed moments of the Riemann zeta function

TL;DR

This paper investigates mixed moments of the Riemann zeta function, establishing asymptotic formulas both unconditionally and under a weaker $abc$ conjecture assumption, advancing understanding of its complex behavior.

Contribution

It provides new asymptotic formulas for mixed moments of the Riemann zeta function, including results under a weaker form of the $abc$ conjecture.

Findings

Validated asymptotic formulas unconditionally

Established results assuming a weaker $abc$ conjecture

Enhanced understanding of the Riemann zeta function's moments

Abstract

We analyse a collection of mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$ conjecture.