Roth's Theorem in the Piatetski-Shapiro primes

2013/04/30 by Mirek, Mariusz
#11B25 #11P55 #42B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.0043

Abstract

Let P denote the set of prime numbers and, for an appropriate function h, define a set P_h=\p\inP: ∃_n∈ℕ p=\lfloor h(n)\rfloor\. The aim of this paper is to show that every subset of P_h having positive relative upper density contains a nontrivial three-term arithmetic progression. In particular the set of Piatetski--Shapiro primes of fixed type 71/72

Related

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• Roth's theorem in the primes
• Roth-type Theorem for high-power system in Piatetski-Shapiro primes (II)
• The Piatetski-Shapiro prime number theorem
• A Density Increment Approach to Roth's Theorem in the Primes