Lower Bounds for the Number of Smooth Values of a Polynomial
| dc.creator | Martin, Greg | |
| dc.date | 1998-07-20 | |
| dc.date | 2002-06-19 | |
| dc.date.accessioned | 2026-07-07T05:25:26Z | |
| dc.date.available | 2026-07-07T05:25:26Z | |
| dc.description | We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial from above, a corresponding lower bound of the correct order of magnitude has hitherto been established only in a few special cases. The purpose of this paper is to provide such a lower bound for an arbitrary polynomial. Various generalizations to subsets of the set of values taken by a polynomial are also obtained. | |
| dc.description | 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with Cecile Dartyge and Gerald Tenenbaum a different approach to the problem was discovered, and the new results superseded the results in this paper. Consequently, this paper has remained unpublished.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 | |
| dc.identifier | https://arxiv.org/abs/math/9807102 | |
| dc.identifier | http://arxiv.org/abs/math/9807102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77178 | |
| dc.subject | Number Theory | |
| dc.subject | 11N32 | |
| dc.title | Lower Bounds for the Number of Smooth Values of a Polynomial | |
| dc.type | text |