Short interval results for a class of arithmetic functions

TL;DR

This paper derives asymptotic formulas for a class of arithmetic functions over short intervals using estimates on Hooley's Δ-function and a short interval Dirichlet hyperbola approach.

Contribution

It introduces a novel method combining Hooley's Δ-function estimates with a short interval Dirichlet hyperbola technique for arithmetic functions.

Findings

Asymptotic formulas for arithmetic functions over short segments

Application of Hooley's Δ-function estimates

Numerous examples demonstrating the results

Abstract

Using estimates on Hooley's $\Delta$-function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also given.