The Landau function and the Riemann Hypothesis

zbMATH Open1481.11005arXiv1907.07664MaRDI QIDQ4989628

Marc Deléglise, Jean Louis Nicolas

Publication date: 25 May 2021

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 $len$. The main result of this article is that the property " For all $n>0$ , $logg(n)<l{i}^{-1}(n))$ " (where $l{i}^{-1}(n)$ denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis.

Full work available at URL: https://arxiv.org/abs/1907.07664

zbMATH Keywords

Riemann hypothesisdistribution of primeshighly composite numberLandau functionchampion number

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25) Software, source code, etc. for problems pertaining to number theory (11-04) Distribution of primes (11N05)

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