A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors

[摘要] Let K be a finite Galois extension of Q. We count primes in short intervals represented by the norm of a prime ideal of K satisfying a small sector condition determined by Hecke characters. We also show that such primes are well-distributed in arithmetic progressions in the sense of Bombieri-Vinogradov. This extends previous work of Duke and Coleman. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Bombieri-Vinogradov;Hecke characters;Hecke L-functions;Norm forms