Patterns of primes in the Sato–Tate conjecture

@article{Gillman2019PatternsOP,
  title={Patterns of primes in the Sato–Tate conjecture},
  author={Nate Gillman and Michael Kural and Alexandru Pascadi and Junyao Peng and Ashwin Sah},
  journal={Research in Number Theory},
  year={2019}
}
Fix a non-CM elliptic curve $E/\mathbb{Q}$, and let $a_E(p) = p + 1 - \#E(\mathbb{F}_p)$ denote the trace of Frobenius at $p$. The Sato-Tate conjecture gives the limiting distribution $\mu_{ST}$ of $a_E(p)/(2\sqrt{p})$ within $[-1, 1]$. We establish bounded gaps for primes in the context of this distribution. More precisely, given an interval $I\subseteq [-1, 1]$, let $p_{I,n}$ denote the $n$th prime such that $a_E(p)/(2\sqrt{p})\in I$. We show $\liminf_{n\to\infty}(p_{I,n+m}-p_{I,n}) < \infty… 
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Primes with Beatty and Chebotarev conditions

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