TL;DR
This paper investigates the properties of exponential and infinitary divisors, focusing on their asymptotic behavior, sum-of-divisors, and totient functions, providing explicit estimates and extremal order results.
Contribution
It offers new insights into the asymptotic behavior and extremal estimates of exponential and infinitary divisors, expanding understanding of modified divisor functions.
Findings
Asymptotic formulas for mean values of divisor functions
Explicit estimates of extremal orders of modified divisors
Analysis of sum-of-divisors and totient functions for exponential and infinitary divisors
Abstract
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the asymptotic behaviour of mean values and explicit estimates of extremal orders.
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