English

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).

Keywords

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

R2 v1 2026-07-01T09:07:09.535Z