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AN ARITHMETIC EQUIVALENCE OF THE RIEMANN HYPOTHESIS
Part of
MARC DELÉGLISE, JEAN-LOUIS NICOLAS
Journal:

Journal of the Australian Mathematical Society / Volume 106 / Issue 2 / April 2019

Published online by Cambridge University Press:

18 June 2018, pp. 235-273

Print publication:

April 2019
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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.