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arXiv · 1903.08715

Multidimensional configurations in the primes with shifted prime steps

Anh Le·Thái Hoàng Lê
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Abstract

Let $\mathcal{P}$ 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 $\mathcal{P}^d$ 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 $1$).

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Anh Le, Thái Hoàng Lê. 2019-03-20. Multidimensional configurations in the primes with shifted prime steps. https://arxiv.org/abs/1903.08715

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