论文标题
关于算术进展中素数的存在
On the existence of products of primes in arithmetic progressions
论文作者
论文摘要
我们研究了基于拉马雷和沃克的工作，研究算术进步中的素数产物。我们的主要结果之一是，如果$ q $是大型模量，那么任何可逆的残基类mod $ q $都包含三个素数的产物，其中每个素数最多为$ q^{6/5+ε} $。我们的论点使用了来自多种领域的结果，例如筛理论或添加剂组合学，以及我们以前在这种情况下尚未使用过的关键成分之一，是希思·布朗（Heath-Brown）在linnik定理上的论文中的素数的结果。
We study the existence of products of primes in arithmetic progressions, building on the work of Ramaré and Walker. One of our main results is that if $q$ is a large modulus, then any invertible residue class mod $q$ contains a product of three primes where each prime is at most $q^{6/5+ε}$. Our arguments use results from a wide range of areas, such as sieve theory or additive combinatorics, and one of our key ingredients, which has not been used in this setting before, is a result by Heath-Brown on character sums over primes from his paper on Linnik's theorem.
