On The Symmetry Of Arithmetical Functions In Almost All Short Intervals, V

TL;DR

This paper investigates the symmetry properties of arithmetic functions within short intervals, focusing on those with non-negative exponential sums, to deepen understanding of their distributional behavior.

Contribution

It introduces new methods to analyze the symmetry of arithmetic functions in short intervals, especially those with non-negative exponential sums, advancing previous research.

Findings

Identifies conditions for symmetry in short intervals

Establishes bounds for arithmetic functions with exponential sums

Provides new insights into the distribution of arithmetic functions

Abstract

We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.