Fractional parts of non-integer powers of primes

Abstract

Let α > 0 be any fixed non-integer, I be any subinterval of [0; 1). In the paper, we prove an analogue of Bombieri-Vinogradov theorem for the set of primes p satisfying the condition {p α } ∈ I. This strengthens the previous result of Gritsenko and Zinchenko.

Bounds for regular induced subgraphs of strongly regular graphs

“…First we note that for P 1 = {p prime; p ≡ 1 (mod 4)}, the set { √ p/2; p ∈ P 1 } is uniformly distributed modulo 1. We can see this result as a direct application of Yip [24, Corollary 6.3], or by a slight adjustment of the arguments in Shubin [21]. In [16], a paper of Balog [4] is cited to contain this result, although no direct statement is given for this specific case.…”