A hybrid of theorems of Vinogradov and Piatetski-Shapiro

Antal Balog and John Benjamin Friedlander

Vol. 156 (1992), No. 1, 45–62

DOI: 10.2140/pjm.1992.156.45

Abstract

It was proved by Vinogradov that every sufficiently large odd integer can be written as the sum of three primes. We show that this remains the case when the primes so utilized are restricted to an explicit thin set. One may take, for example, the “Piatetski-Shapiro primes” p = [n^1∕γ] with any γ > 20∕21. By a similar argument it would follow that, for arbitrary 𝜃, 0 < 𝜃 < 1, and suitable λ = λ(𝜃) > 0, one may take the set of primes for which {p^𝜃} < p^−λ.

Mathematical Subject Classification 2000

Primary: 11P32

Secondary: 11N05

Milestones

Received: 14 April 1991

Published: 1 November 1992