no. 2
On the fractional parts of x/n and related sequences. II
Annales de l'Institut Fourier, Volume 27 (1977) no. 2, pp. 1-30

As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of xh(x) where h is an arithmetical function (namely h(n)=1/n, h(n)=logn, h(n)=1/logn) and n is an integer (or a prime order) running over the interval [y(x),x)]. The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.

Comme promis dans l’article no I de même titre (Ann. Inst. Fourier, 26-4 (1976), 115-131), nous étudions ici la répartition asymptotique des parties fractionnaires de xh(n) où h est une fonction arithmétique (à savoir h(n)=1/n, h(n)=logn, h(n)=1/logn) et n un entier (ou un nombre premier) parcourant l’intervalle [y(x),x)]. On s’est efforcé de démontrer des formes assez fines des théorèmes, encore que certains résultats se prêtent à des améliorations au prix d’une technicité accrue. Des applications arithmétiques seront données plus tard.

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Saffari, Bahman; Vaughan, R. C. On the fractional parts of $x/n$ and related sequences. II. Annales de l'Institut Fourier, Volume 27 (1977) no. 2, pp. 1-30. doi: 10.5802/aif.649

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