For gamma sufficiently close to 1, Piatetski-Shapiro primes satisfy discorrelation with nilsequences, giving asymptotics for finite-complexity linear systems and infinitely many k-term APs when gamma exceeds 1 minus 2 to the minus Ck.
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Linear equations in Piatetski-Shapiro primes
For gamma sufficiently close to 1, Piatetski-Shapiro primes satisfy discorrelation with nilsequences, giving asymptotics for finite-complexity linear systems and infinitely many k-term APs when gamma exceeds 1 minus 2 to the minus Ck.