Almost-prime values of polynomials at prime arguments

作者：Irving A J^*

来源：Bulletin of the London Mathematical Society, 2015, 47(4): 593-606.

DOI：10.1112/blms/bdv035

We consider almost-primes of the form f(p) where f is an irreducible polynomial over Z and p runs over primes. We improve a result of Richert for polynomials of degree at least 3. In particular, we show that, when the degree is large, there are infinitely many primes p for which f(p) has at most deg f + O(log deg f) prime factors.

• 出版日期2015-8