On a relation to the Riemann Hypothesis and an analytic part for the divisor function

Hideto Iwata

doi:10.48550/arxiv.2601.11052

On a relation to the Riemann Hypothesis and an analytic part for the divisor function

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Hideto Iwata

DOI: 10.48550/arxiv.2601.11052

Cited by: 0

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).

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories Limits and Structures in Graph Theory

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 16 January 2026
Document type: Preprint