The Landau function and the Riemann Hypothesis

2019/07/17 by Marc Deléglise, Deleglise, Marc, Jean-Louis Nicolas +1
Mathematics · #11-04 (Secondary) #11A25 (Primary) #11N05 #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1907.07664

openalex publication_date 2019/07/17 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28

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 n > 0 , log g(n) < li^-1 (n)) " (where li^-1(n) denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis.

Citations

• Highly Composite Numbers

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