# 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…
3 Citations
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