多项式光滑值个数的下界
数论
2007-05-23 v2
摘要
我们研究如下问题：证明给定多项式的值在正向比例的时间内是光滑的（即没有大素因子）。尽管存在一些从上方界定多项式光滑值个数的结果，但具有正确数量级的相应下界迄今仅在少数特殊情形中被建立。本文的目的是为任意多项式提供这样的下界。也得到了对多项式所取值集合的子集的多种推广。
引用
@article{arxiv.math/9807102,
title = {Lower Bounds for the Number of Smooth Values of a Polynomial},
author = {Greg Martin},
journal= {arXiv preprint arXiv:math/9807102},
year = {2007}
}
备注
24 pages. During the submission process, in communication with Cecile Dartyge and Gerald Tenenbaum a different approach to the problem was discovered, and the new results superseded the results in this paper. Consequently, this paper has remained unpublished. Our article appeared as "Polynomial Values Free of Large Prime Factors" in Periodica Math. Hungarica 43 (2001), no. 1-2, 111-119