k-fold sums from a set with few products
| dc.creator | Croot, Ernie | |
| dc.creator | Hart, Derrick | |
| dc.date | 2009-04-04 | |
| dc.date | 2009-04-15 | |
| dc.date.accessioned | 2026-07-07T13:03:37Z | |
| dc.date.available | 2026-07-07T13:03:37Z | |
| dc.description | In the present paper we show that if A is a set of n real numbers, and the product set A.A has at most n^(1+c) elements, then the k-fold sumset kA has at least n^(log(k/2)/2 log 2 + 1/2 - f_k(c)) elements, where f_k(c) -> 0 as c -> 0. We believe that the methods in this paper might lead to a much stronger result; indeed, using a result of Trevor Wooley on Vinogradov's Mean Value Theorem and the Tarry-Escott Problem, we show that if |A.A| < n^(1+c), then |k(A.A)| > n^(Omega((k/log k)^(1/3))), for c small enough in terms of k (we believe that a certain modification of this argument can perhaps produce similar conclusions for kA). | |
| dc.description | 19 pages. Final draft -- light corrections, submitted to Siam J. of Discrete Math | |
| dc.identifier | https://arxiv.org/abs/0904.0718 | |
| dc.identifier | http://arxiv.org/abs/0904.0718 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226870 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11B99 | |
| dc.title | k-fold sums from a set with few products | |
| dc.type | text |