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AN ANALOGUE OF THE ROBIN INEQUALITY OF THE SECOND TYPE FOR ODD INTEGERS
Keywords:
Robin inequality, Riemann hypothesisDOI:
https://doi.org/10.17654/0972555522023Abstract
In this paper, we give a variant of the Robin inequality which states that $\frac{\sigma(n)}{n} \leq \frac{e^\gamma}{2} \log \log n+\frac{0.7398 \cdots}{\log \log n}$ for all odd integers $n \geq 3$.
Received: March 7, 2022
Accepted: May 30, 2022
References
T. Oshiro, Refinement of Robin’s inequality for odd integers, Bachelor Thesis, Yokohama City University, 2022 (in Japanese).
G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. (9) 63 (1984), 187-213.
E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., Revised by D. R. Heath-Brown, Oxford, 1986.
C. L. Washington and A. Yang, Analogues of the Robin-Lagarias criteria for the Riemann hypothesis, Int. J. Number Theory 17(4) (2021), 843-870.
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