On the size of $k$-fold sum and product sets of integers
| dc.creator | Bourgain, Jean | |
| dc.creator | Chang, Mei-Chu | |
| dc.date | 2003-09-03 | |
| dc.date.accessioned | 2026-07-07T05:00:49Z | |
| dc.date.available | 2026-07-07T05:00:49Z | |
| dc.description | We prove the following theorem: for all positive integers $b$ there exists a positive integer $k$, such that for every finite set $A$ of integers with cardinality $|A| > 1$, we have either $$ |A + ... + A| \geq |A|^b$$ or $$ |A \cdot ... \cdot A| \geq |A|^b$$ where $A + ... + A$ and $A \cdot ... \cdot A$ are the collections of $k$-fold sums and products of elements of $A$ respectively. This is progress towards a conjecture of Erdös and Szemerédi on sum and product sets. | |
| dc.description | 33 pages, no figures, submitted, J. Amer. Math. Soc. (Proxy submission) | |
| dc.identifier | https://arxiv.org/abs/math/0309055 | |
| dc.identifier | http://arxiv.org/abs/math/0309055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68459 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11P70 | |
| dc.title | On the size of $k$-fold sum and product sets of integers | |
| dc.type | text |