## Abstract

We establish a joint distribution result concerning the fractional part of (Formula presented.) for (Formula presented.), where p is a prime satisfying a Chebotarev condition in a fixed finite Galois extension over (Formula presented.). As an application, for a fixed non-CM elliptic curve (Formula presented.), an asymptotic formula is given for the number of primes at the extremes of the Sato–Tate measure modulo a large prime ℓ. These are precisely the primes p for which the Frobenius trace (Formula presented.) satisfies the congruence (Formula presented.). We assume a zero-free region hypothesis for Dedekind zeta functions of number fields.

Original language | English (US) |
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Pages (from-to) | 595-619 |

Number of pages | 25 |

Journal | Mathematika |

Volume | 68 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2022 |

## All Science Journal Classification (ASJC) codes

- General Mathematics

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