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AN ARITHMETIC EQUIVALENCE OF THE RIEMANN HYPOTHESIS
Published online by Cambridge University Press: 18 June 2018
Abstract
Let $h(n)$ denote the largest product of distinct primes whose sum does not exceed
$n$. The main result of this paper is that the property for all
$n\geq 1$, we have
$\log h(n)<\sqrt{\text{li}^{-1}(n)}$ (where
$\text{li}^{-1}$ denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis.
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- Research Article
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- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
Footnotes
Research partially supported by CNRS, Institut Camille Jordan, UMR 5208.
References
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