Vinogradov's three primes theorem with almost twin primes

Kaisa Matomäki, Xuancheng Shao

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper we prove two results concerning Vinogradov's three primes theorem with primes that can be called almost twin primes. First, for any m, every sufficiently large odd integer N can be written as a sum of three primes p1, p2 and p3 such that, for each i ϵ (1, 2, 3), the interval [pi, pi + H] contains at least m primes, for some H = H(m). Second, every sufficiently large integer N Ξ 3 (mod 6) can be written as a sum of three primes p1, p2 and p3 such that, for each i ϵ (1, 2, 3), pi + 2 has at most two prime factors.

Original languageEnglish
Pages (from-to)1220-1256
Number of pages37
JournalCompositio Mathematica
Volume153
Issue number6
DOIs
StatePublished - Jun 1 2017

Bibliographical note

Publisher Copyright:
© Foundation Compositio Mathematica 2017.

Keywords

  • Bohr sets
  • Vinogradov's theorem
  • sieve method
  • transference principle
  • twin primes

ASJC Scopus subject areas

  • Algebra and Number Theory

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