Almost-primes represented by quadratic polynomials
Almost-primes represented by quadratic polynomials
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DOI：
10.4064/aa151-3-2
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发表时间：
2012
期刊：
影响因子：
0.7
通讯作者：
R. Oliver
中科院分区：
文献类型：
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作者：
R. Oliver
设G(X)是整系数的不可约多项式。猜想集合{n∈N：G(N)是素数}对大多数G(X)都是无穷的。如果Pr表示至多具有r个素数因子的无平方正整数集，我们考虑集合{n∈N：g(N)∈Pr}，目的是证明对于r的适当选择它是无穷的。关于这个问题，人们已经做了大量的工作，最显著的结果是Iwaniec，BuhšTab和Richert。这里我们证明了，如果deg(G(X))=2，那么我们可以取r=2。
Let G(x) be an irreducible polynomial with integer coefficients. It is conjectured that the set {n ∈ N : G(n) is prime} is infinite for most G(x). If Pr denotes the set of squarefree positive integers with at most r prime factors, we consider the set {n ∈ N : G(n) ∈ Pr} with the goal of showing that it is infinite for a suitable choice of r. Considerable work has been done on this problem, with the most notable results being due to Iwaniec, Buhštab, and Richert. Here we show that if deg(G(x)) = 2, then we may take r = 2.