题目：Primes in Arithmetic Progressions with Friable Indices and Applications

报告人：吴杰 教授 （CNRS, Université Paris-Est Créteil）

地点：致远楼101室

时间：2019年4月23日 9:00-10:00

摘要：

In this talk, we shall present our recent works on primes in arithmetic progressions with friable indices, joint with Jianya Liu and Ping Xi. Denote by $/pi(x,y;q,a)$ the number of primes $p/leqslant x$ such that $p/equiv a/bmod q$ and $(p-a)/q$ is free of prime factors larger than $y$. Assume a suitable form of Elliott--Halberstam conjecture, it is proved that $/pi(x,y;q,a)$ is asymptotic to $/rho(/log(x/q)//log y)/pi(x)//varphi(q)$ on average, subject to certain ranges of $y$ and $q$, where $/rho$ is the Dickman function. Moreover, unconditional upper bounds are also obtained via sieve methods.

As applications, we shall consider the following two problems :

1) the number of shifted primes with large prime factors,

2) friable variant of the Titchmarsh divisor problem.

欢迎各位师生参加！