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

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

D(N):=sup 0≤γ≤0 |∑ p≤/N p α ≤γ 1-π(N)γ|
de la suite (p α ), lorsque 5/3≤α>3 et α≠2.

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

D(N):=sup 0≤γ≤0 |∑ p≤/N p α ≤γ 1-π(N)γ|
for the sequence (p α ), when 5/3≤α>3 and α≠2.

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     author = {Xiaodong Cao and Wenguang Zhai},
     title = {On the distribution of $p^\alpha $ modulo one},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {407--423},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {2},
     year = {1999},
     zbl = {0988.11027},
     mrnumber = {1745887},
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Xiaodong Cao; Wenguang Zhai. On the distribution of $p^\alpha $ modulo one. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 2, pp. 407-423. https://jtnb.centre-mersenne.org/item/JTNB_1999__11_2_407_0/

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