On the distribution of p α modulo one
Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 2, pp. 407-423.

In this paper, we give a new upper-bound for the discrepancy

D(N):=sup 0γ0 | p/N p α γ 1-π(N)γ|
for the sequence (p α ), when 5/3α>3 and α2.

Dans cet article, on donne une nouvelle majoration de la discrépance

D(N):=sup 0γ0 | p/N p α γ 1-π(N)γ|
de la suite (p α ), lorsque 5/3α>3 et α2.

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     title = {On the distribution of $p^\alpha $ modulo one},
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Cao, Xiaodong; Zhai, Wenguang. On the distribution of $p^\alpha $ modulo one. Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 2, pp. 407-423. http://www.numdam.org/item/JTNB_1999__11_2_407_0/

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