Divisor and Totient Functions Estimates

TL;DR

This paper provides new unconditional estimates for divisor and totient functions, aligning with the Riemann hypothesis, and addresses the Nicolas inequality for large integers.

Contribution

It introduces novel unconditional bounds for divisor and totient functions, advancing understanding of their behavior and implications for the Nicolas inequality.

Findings

Estimates are consistent with the Riemann hypothesis.

Results suggest the Nicolas inequality holds for large integers.

Provides new bounds that improve previous results.

Abstract

New unconditional estimates of the divisor and totient functions are contributed to the literature. These results are consistent with the Riemann hypothesis and seem to solve the Nicolas inequality for all sufficiently large integers.