Geodesic
On the distribution of αpk modulo 1
Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 121-130

Voir la notice de l'article provenant de la source Cambridge University Press

The fractional part of the sequence {αnk}, where α is an irrational real number and k is an integer, was first studied early this century, initiated by the work of Hardy, Littlewood and Weyl. It seems very natural to consider the subsequence {αpk}, where p denotes a prime variable. The pioneering work in this direction was conducted by Vinogradov [13,14]. Improvements have since been made by Vaughan [12], Ghosh [4], Harman [6,7,8] and Jia [11]. The best results to date have been obtained by Harman for k = 1 [9], by Baker and Harman for 2 ≤ k ≤ 12 [1], and by Harman for larger k [8]. In the following work, we shall adopt a sieve technique developed by Harman in [6] to show the following. 
Wong, K. C. On the distribution of αpk modulo 1. Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 121-130. doi: 10.1017/S0017089500032018
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