Multidimensional configurations in the primes with shifted prime steps

2019/03/20 by Anh N. Le, Le, Anh, Thái Hoàng Lê +1
Mathematics · #Limits and Structures in Graph Theory #Analytic Number Theory Research #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1903.08715

Abstract

Let P denote the set of primes. For a fixed dimension d, Cook-Magyar-Titichetrakun, Tao-Ziegler and Fox-Zhao independently proved that any subset of positive relative density of P^d contains an arbitrary linear configuration. In this paper, we prove that there exists such configuration with the step being a shifted prime (prime minus 1 or plus 1).

Related

• Polynomial configurations in dense subsets of the prime lattice
• Random linear configurations in dense sets and primes
• Narrow arithmetic progressions in the primes
• On van der Corput property of shifted primes
• Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes