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

Hideto Iwata

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arXiv · 2601.11052

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

Hideto Iwata

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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).

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Hideto Iwata. 2026-01-16. On a relation to the Riemann Hypothesis and an analytic part for the divisor function. https://arxiv.org/abs/2601.11052

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