Approximating the divisor functions

TL;DR

This paper introduces a novel approach to approximate divisor functions using a sequence of functions and an analytical delta-like sequence, providing a new proof of Gronwall's theorem on their asymptotic behavior.

Contribution

It presents a new proof of Gronwall's theorem by combining approximation techniques with delta-like sequences, advancing understanding of divisor functions.

Findings

New proof of Gronwall's theorem established

Approximation methods effectively analyze divisor functions

Analytical delta-like sequences enhance asymptotic analysis

Abstract

We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor functions.