The Landau function and the Riemann hypothesis

Abstract : The Landau function g(n) is the maximal order of an element of the symmetric group of degree n; it is also the largest product of powers of primes whose sum is ≤ n. The main result of this article is that the property " For all ≥ 1, log g(n) < sqrt( li −1 (n)) " (where li-1 denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis.
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Submitted on : Monday, July 8, 2019 - 7:34:53 PM
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Marc Deléglise, Jean-Louis Nicolas. The Landau function and the Riemann hypothesis. 2019. ⟨hal-02177338⟩

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