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On S\'ark\"ozy's theorem for shifted primes

Number Theory 2023-08-24 v3 Combinatorics
Authors: Ben Green
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Abstract

Suppose that A⊂{1,…,N}A \subset \{1,\dots, N\} has no two elements differing by p−1p-1, pp prime. Then ∣A∣≪N1−c|A| \ll N^{1 - c}.

Keywords

sárközy theorem shifted primes difference set additive combinatorics

Cite

@article{arxiv.2206.08001,
  title  = {On S\'ark\"ozy's theorem for shifted primes},
  author = {Ben Green},
  journal= {arXiv preprint arXiv:2206.08001},
  year   = {2023}
}

Comments

104 pages, accepted for publication in JAMS. v3 incorporates some corrections drawn to my attention by the referees

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