粗粒度整数-平滑？不爽？都是！
Coarse-grained integers - Smooth? Rough? Both!
摘要：
我们计数[B，C]-粒度的k-因子整数，它们同时是B-粗糙和C-光滑的，并且有固定数量的k个素因子。我们的目标是利用明确的版本的素数定理尽可能多地得到良好的显式界的计数，这样的整数。这一分析受到了一般数域筛法中某些内在过程的启发。结果至少应该提供一些关于那里发生了什么的见解。我们估计的一些递归定义的函数的计数。由于它们仍然难以处理，只有另一个近似步骤才能揭示它们的顺序。最后，我们使用所获得的界限进行数值实验，显示如何良好的所需的计数可以近似为参数的一般数场筛在上述令人鼓舞的应用。
英文摘要：
We count ]B, C]-grained, k-factor integers which are simultaneously B-rough and C-smooth and have a fixed number k of prime factors. Our aim is to exploit explicit versions of the prime number theorem as much as possible to get good explicit bounds for the count of such integers. This analysis was inspired by certain inner procedures in the general number field sieve. The result should at least provide some insight in what happens there. We estimate the given count in terms of some recursively defined functions. Since they are still difficult to handle, only another approximation step reveals their orders. Finally, we use the obtained bounds to perform numerical experiments that show how good the desired count can be approximated for the parameters of the general number field sieve in the mentioned inspiring application.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
