D{\'e}monstration d'une conjecture de Kruyswijk et Meijer sur le plus petit d{\'e}nominateur des nombres rationnels d'un intervalle

Michel Balazard; Bruno Martin

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arXiv · 2303.01303

D{\'e}monstration d'une conjecture de Kruyswijk et Meijer sur le plus petit d{\'e}nominateur des nombres rationnels d'un intervalle

Michel Balazard·Bruno Martin

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Abstract

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

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Michel Balazard, Bruno Martin. 2023-03-02. D{\'e}monstration d'une conjecture de Kruyswijk et Meijer sur le plus petit d{\'e}nominateur des nombres rationnels d'un intervalle. https://arxiv.org/abs/2303.01303

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