A Combinatorial Method for Counting Smooth Numbers in Sets of Integers
| dc.creator | Croot, Ernie | |
| dc.date | 2003-11-13 | |
| dc.date | 2003-11-26 | |
| dc.date.accessioned | 2026-07-07T05:02:52Z | |
| dc.date.available | 2026-07-07T05:02:52Z | |
| dc.description | In this paper we present a method for producing asymptotic estimates for the number of integers in a given S having only ``small'' prime factors. The conditions that need to be verified are simpler than those required by other methods, and we apply our result to give an easy proof of a result which says that dense subsets A and B of {1,2,...,x} always produce asymptotically the expected number of x^r - smooth sums a+b, where a in A and b in B. Recall that a number n is said to be y-smooth if all its prime divisors are at most y. | |
| dc.description | Light Corrections | |
| dc.identifier | https://arxiv.org/abs/math/0311226 | |
| dc.identifier | http://arxiv.org/abs/math/0311226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69184 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11N25 | |
| dc.title | A Combinatorial Method for Counting Smooth Numbers in Sets of Integers | |
| dc.type | text |