Twisted mixed moments of the Riemann zeta function

TL;DR

This paper investigates twisted mixed moments of the Riemann zeta function, deriving asymptotic formulas with secondary terms, both unconditionally and assuming a weaker $abc$-conjecture, advancing understanding of zeta function behavior.

Contribution

It provides new asymptotic formulas for twisted mixed moments of the Riemann zeta function, including secondary terms, under weaker conjectural assumptions.

Findings

Established asymptotic formulas with secondary terms for twisted moments

Validated formulas both unconditionally and under a weaker $abc$-conjecture

Enhanced understanding of the Riemann zeta function's moments

Abstract

We analyse a collection of twisted mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae comprising on some instances secondary terms of the shape $P(\log T) T^{C}$ for a suitable constant $C<1$ and a polynomial $P(x)$. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$-conjecture.