Démonstration d'une conjecture de Kruyswijk et Meijer sur le plus petit dénominateur des nombres rationnels d'un intervalle

2023/03/02 by Michel Balazard, Balazard, Michel, Bruno Martin +1 · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.01303

openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The average value of the smallest denominator of a rational number belonging to the interval ](j-1)/N,j/N], where~j=1,…, N, is proved to be asymptotically equivalent to~16π^-2√(N), when N tends to infinity. The result had been conjectured in 1977 by Kruyswijk and Meijer.

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