标题:Primes in arithmetic progressions with friable indices
作者:Liu J.; Wu J.; Xi P.
作者机构:[Liu, J] School of Mathematics, Shandong University, Jinan, 250100, China;[ Wu, J] CNRS LAMA 8050, Université Paris-Est Créteil, Créteil Cedex, 94010, 更多
通讯作者:Wu, J(jie.wu@math.cnrs.fr)
通讯作者地址:[Wu, J] CNRS LAMA 8050, Université Paris-Est CréteilFrance;
来源:Science China Mathematics
出版年:2019
DOI:10.1007/s11425-018-9480-6
关键词:11N05; 11N13; 11N25; 11N36; friable numbers; primes in arithmetic progression; shifted primes; sieve
摘要:We consider the number π(x, y; q, a) of primes p ≤ x such that p ≡ a (mod q) and (p − a)/q is free of prime factors greater than y. Assuming a suitable form of Elliott-Halberstam conjecture, it is proved that π(x, y; q, a) is asymptotic to ρ(log(x/q)/log y)π(x)/φ(q) on average, subject to certain ranges of y and q, where ρ is 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. © 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.
收录类别:SCOPUS
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85061735047&doi=10.1007%2fs11425-018-9480-6&partnerID=40&md5=cad6fe37a796056ccc9813e72a14a1b8
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