Primes in arithmetic progressions with friable indices
Primes in arithmetic progressions with friable indices
复制标题
具有易碎指数的算术级数中的素数
DOI：
10.1007/s11425-018-9480-6
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Xi Ping
中科院分区：
文献类型：
--
作者：
Liu Jianya;Wu Jie;Xi Ping
We consider the numberπ(x, y; q, a)of primesp⩽xsuch thatp≡a(modq) and (p−a)/qis free of prime factors greater than y. Assuming a suitable form of Elliott-Halberstam conjecture, it is proved thatπ(x, y; q, a)is asymptotic toρ(log(x/q)/logy)π(x)/φ(q)on average, subject to certain ranges ofyandq, whereρis the Dickman function. Moreover, unconditional upper bounds are also obtained via sieve methods. As a typical application, we may control more effectively the number of shifted primes with large prime factors.
