摘要 : In this article, we study some variants of the Bombieri-Vinogradov theorem for number fields. We refine the level of distribution in the previous work of Murty-Petersen. When investigating the short interval version, we give a new... 展开 In this article, we study some variants of the Bombieri-Vinogradov theorem for number fields. We refine the level of distribution in the previous work of Murty-Petersen. When investigating the short interval version, we give a new zero density estimate of large sieve type, unlike the result of Hinz which is directly used in Thorner's work. Further, we strengthen the result of Thorner for the Bombieri-Vinogradov theorem in short intervals. As applications, we improve some numerical results on the bounded gaps of primes in Chebotarev sets and the Euclidean algorithm for S-integers. 收起