The divisor function and divisor problem

TL;DR

This paper explores classical and recent divisor problems, highlighting their connections with the moments of the Riemann zeta function, and discusses Erdős's contributions and recent developments in the field.

Contribution

It provides a comprehensive overview of divisor problems, including historical context, recent results, and their links to the moments of the Riemann zeta function.

Findings

Discussion of Erdős's divisor problems

Recent results on divisor problems

Connections with moments of | ilde{ ext{zeta}}(1/2+it)|

Abstract

The purpose of this text is twofold. First we discuss some divisor problems involving Paul Erd\H os (1913-1996), whose centenary of birth is this year. In the second part some recent results on divisor problems are discussed, and their connection with the powers moments of $|\zeta(\frac{1}{2}+it)|$ is pointed out. This is an extended version of the lecture given at the conference ERDOS100 in Budapest, July 1-5, 2013.