The Green-Tao theorem for Piatetski-Shapiro primes

Abstract

Let $m\ge 3$. Suppose that $$1-2^{-2^{m^2{4}^m}}<\gamma <1.$$ Then the set $$\{p\text{ prime}:p=[n^{\frac{1}{\gamma }}]\text{ for some }n\in \mathbb{N}\}$$ contains infinitely many non-trivial $m$-term arithmetic progressions.

This is a preliminary draft, which maybe contains some mistakes

Cited by in corpus (2)

• Distributions of Finite Sequences Represented by Polynomials in Piatetski-Shapiro Sequences
• A transference principle for systems of linear equations, and applications to almost twin primes