Let K be a finite Galois extension of $\mathbb{Q}$. 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.

中文翻译：

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短间隔和小扇区中素数的 Bombieri-Vinogradov 定理

令K为有限伽罗瓦扩展$\mathbb{问}$. 我们在由满足由赫克字符确定的小扇区条件的K的素理想范数表示的短间隔内计算素数。我们还表明，在 Bombieri-Vinogradov 的意义上，这样的质数在等差数列中分布良好。这扩展了杜克和科尔曼之前的工作。