Abstract We combine A.J. Irving's sieve method with the Diamond-Halberstam-Richert (DHR) sieve to study the almost-prime values produced by products of irreducible polynomials evaluated at prime arguments. A significant improvement is made when the degrees of the irreducible components are large compared with the number of components themselves. This generalizes the previous results of Irving and Kao, who separately examined the almost-prime values of a single irreducible polynomial evaluated at prime arguments.

中文翻译：

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素数参数处可约多项式的近似素数

摘要 我们将AJ Irving 的筛法与Diamond-Halberstam-Richert (DHR) 筛法相结合，研究以素数参数求值的不可约多项式的乘积所产生的几乎素数。当不可约分量的度数与分量本身的数量相比较大时，则取得了显着的改善。这概括了 Irving 和 Kao 之前的结果，他们分别检查了以素数参数计算的单个不可约多项式的几乎素数。