A Tauberian theorem for Ingham summation method

TL;DR

This paper proves a Tauberian theorem for the Ingham summation method and applies it to analyze the asymptotic behavior of mean values of multiplicative functions.

Contribution

It introduces a new Tauberian theorem specific to Ingham summation and demonstrates its application to multiplicative number theory.

Findings

Established a Tauberian theorem for Ingham summation.

Applied the theorem to derive asymptotics of multiplicative functions.

Provided new tools for analyzing summability in number theory.

Abstract

The aim of this work is to prove a Tauberian theorem for the Ingham summability method. The Tauberian theorem we prove is then applied to analyze asymptotics of mean values of multiplicative functions on natural numbers.