Work

Lower Bounds on Expressions Depending on the Functions φ(n), ψ(n) and σ(n): Part 4

Year: 2026

Type: article

Abstract: In this article, we establish four lower-bound inequalities for rational expressions involving the Euler totient function φ(n), the Dedekind psi function ψ(n), and the sum-of-divisors function σ(n). The inequalities concern rational expressions involving sums of cubes, products of these arithmetic functions, and sums of pairs of these functions. The lower bounds are given explicitly as rational functions of n and are attained when n is prime. Furthermore, we formulate four conjectures that extend the established inequalities to arbitrary positive integer powers k.

Source: Mathematics

DOI: 10.3390/math14213935

Authors: Stoyan Dimitrov, Meglena Lazarova

Institutions: Technical University of Sofia, Prof. Assen Zlatarov University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: European Regional Development Fund