This article is cited in 12 papers

Primes in Special Intervals and Additive Problems with Such Numbers

M. E. Changa

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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 $E$.

UDC: 511

Received: 25.06.2002

DOI: 10.4213/mzm192

 English version: Mathematical Notes, 2003, 73:3, 389–401

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