no. 2
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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     title = {On the distribution of $p^\alpha $ modulo one},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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     year = {1999},
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     url = {http://www.numdam.org/item/JTNB_1999__11_2_407_0/}
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Cao, Xiaodong; Zhai, Wenguang. On the distribution of $p^\alpha $ modulo one. Journal de Théorie des Nombres de Bordeaux, Tome 11 (1999) no. 2, pp. 407-423. http://www.numdam.org/item/JTNB_1999__11_2_407_0/

[1] R C. Baker, G. Kolesnik, On the distribution of pα modulo one, J. Reine Angew. Math. 356 (1985), 174-193. | Zbl 0546.10027

[2] A. Balog, On the fractional part of pθ, Arch. Math. 40 (1983), 434-440. | Zbl 0517.10038

[3] A. Balog, On the distribution of pθ (mod1), Acta. Math. Hungar. 45 (1985), 179-199 | Zbl 0571.10038

[4] E. Bombieri and H. Iwaniec, On the order of ζ(1/2 + it), Ann. Scuola Norm. Sup. Pisa. 13 (1986), 449-472. | Numdam | Zbl 0615.10047

[5] E. Fouvry, H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. | MR 1027058 | Zbl 0687.10028

[6] S.A. Gritsenko, On a problem of I. M. Vinogradov (in Russian), Mat. Zametki 39 (1986), 625-650 | MR 850799 | Zbl 0612.10029

[7] G. Harman, On the distribution of √p modulo one, Mathematika 30 (1983), 104-110. | Zbl 0504.10019

[8] Heath-Brown, D. R. Heath-Brown, The Pjatecskil-Sapiro prime number theory, J. Number Theory 16 (1983), 242-266. | MR 698168 | Zbl 0513.10042

[9] R.M. Kaufman, The distribution of √p, Mat. Zametki 26 (1979), 497-504 | Zbl 0417.10030

[10] Leitmann, On the distribution of some sequences, J. London Math. Soc. 14 (1976), 430-432. | MR 432566 | Zbl 0343.10025

[11] H.-Q. Liu, On the number of abelian groups of a given order(supplement), Acta Arith. 64 (1993), 285-296. | MR 1225430 | Zbl 0790.11074

[12] E.C. Titchmarsh, The Theory of Riemann Zeta Function, Oxford, 1951. | MR 46485 | Zbl 0042.07901

[13] R.C. Vaughan, The Hardy-Littlewood Method, Cambridge, 1981. | MR 628618 | Zbl 0455.10034

[14] I.M. Vinogradov, Special Variants of the Method of Trigonometric sums (in Russian), Izda. Nauka, Moskow, 1976. | MR 469878 | Zbl 0429.10023