On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions

TL;DR

This paper investigates lower bounds for the error term in asymptotic formulas for specific arithmetic functions generated by Dirichlet series involving products of Riemann zeta-functions, addressing a question posed by A. Schinzel.

Contribution

It provides new omega estimates for the remainder term of a class of arithmetic functions linked to special Dirichlet series, advancing understanding of their asymptotic behavior.

Findings

Established lower bounds for the remainder term

Analyzed functions generated by products of Riemann zeta-functions

Extended previous results on asymptotic estimates

Abstract

The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series which involves a product of Riemann zeta-functions of a special form.