A BOMBIERI–VINOGRADOV THEOREM FOR NUMBER FIELDS. Issue 3 (25th June 2021) - Jiang, Yujiao
Abstract: 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.