Linear inequalities in primes

@article{Walker2021LinearII,
  title={Linear inequalities in primes},
  author={Aled Walker},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2021}
}
  • A. Walker
  • Published 15 January 2019
  • Mathematics
  • Journal d'Analyse Mathématique
In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic coefficients. For $m$ simultaneous inequalities we require at least $m+2$ variables, improving upon existing methods, which require at least $2m+1$ variables. Our result also generalises the theorem of Green and Tao on linear equations in primes. Many of the methods presented apply for arbitrary coefficients, not just for algebraic coefficients… 
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