Comparison of probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions

TL;DR

This paper compares probabilistic and exact approaches for analyzing the asymptotic behavior of summation arithmetic functions, providing new theorems on standard deviation estimates under broad stationarity conditions.

Contribution

It introduces new theoretical results on the estimation of standard deviation for specific summation functions satisfying broad stationarity conditions.

Findings

Proved lemmas and theorems on standard deviation estimation

Established conditions for broad-sense stationarity in summation functions

Compared probabilistic and exact methods for asymptotic analysis

Abstract

The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are investigated for summation arithmetic functions. A lemma and theorems about the estimation of the standard deviation for the summation arithmetic Mertens and Lowville functions completely satisfying the stationarity conditions in the broad sense are proved.