On sums and products in C[x]
| dc.creator | Croot, Ernie | |
| dc.creator | Hart, Derrick | |
| dc.date | 2008-12-12 | |
| dc.date | 2009-04-14 | |
| dc.date.accessioned | 2026-07-07T13:03:10Z | |
| dc.date.available | 2026-07-07T13:03:10Z | |
| dc.description | We show that under the assumption of a 24-term version of Fermat's Last Theorem, there exists an absolute constant c > 0 such that if S is a set of n > n_0 positive integers satisfying |S.S| < n^(1+c), then the sumset S.S satisfies |S+S| >> n^2. In other words, we prove a weak form of the Erdos-Szemeredi sum-product conjecture, conditional on an extension of Fermat's Last Theorem. Unconditionally, we prove this theorem for when S is a set of n monic polynomials. We also prove an analogue of a theorem of Bourgain and Chang for the ring C[x]. | |
| dc.description | We added a conditional theorem to the paper, which holds under a certain generalization of Fermat's Last Theorem; and, we added an acknowledgment (to Jozsef Solymosi) | |
| dc.identifier | https://arxiv.org/abs/0812.2286 | |
| dc.identifier | http://arxiv.org/abs/0812.2286 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226701 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11B75 | |
| dc.title | On sums and products in C[x] | |
| dc.type | text |