Geodesic
Primes in Special Intervals and Additive Problems with Such Numbers
Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 423-436 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study primes in a special set $E$ which is naturally described by the fractional part of $p^a$, where $a<1$ is a noninteger. An asymptotic formula with power lowering in the remainder of the trigonometric sum over primes from the set $E$ is obtained. We study several applications of this result to problems of the distribution of primes from $E$ in arithmetic progressions and to additive problems with primes from $E$. 
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     title = {Primes in {Special} {Intervals} and {Additive} {Problems} with {Such} {Numbers}},
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M. E. Changa. Primes in Special Intervals and Additive Problems with Such Numbers. Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 423-436. http://geodesic.mathdoc.fr/item/MZM_2003_73_3_a8/

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