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A BOMBIERI–VINOGRADOV THEOREM FOR NUMBER FIELDS
Author(s) -
Jiang Yujiao,
Lü Guangshi,
Wang Zihao
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12096
Subject(s) - mathematics , sieve (category theory) , bounded function , discrete mathematics , interval (graph theory) , euclidean geometry , distribution (mathematics) , combinatorics , mathematical analysis , geometry
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.