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On the distribution of p α modulo one

Xiaodong Cao, Wenguang Zhai (1999)

Journal de théorie des nombres de Bordeaux

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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