On a relation to the Riemann Hypothesis and an analytic part for the divisor function
Number Theory
2026-01-19 v1
Abstract
Let phi(n) denote the Euler totient function. We study the analytic part associated with the summatory function of sigma_1(n) and obtain explicit bounds under the Riemann Hypothesis. In particular, we establish an upper bound of order x^{delta'} exp((log x)/(log log x)), where delta' = max(1/2, delta).
Cite
@article{arxiv.2601.11052,
title = {On a relation to the Riemann Hypothesis and an analytic part for the divisor function},
author = {Hideto Iwata},
journal= {arXiv preprint arXiv:2601.11052},
year = {2026}
}
Comments
11 pages Submitted to Acta Arithmetica