On some power sum problems of Montgomery and Turan
| dc.creator | Andersson, Johan | |
| dc.date | 2007-06-28 | |
| dc.date | 2007-07-11 | |
| dc.date.accessioned | 2026-07-07T08:14:46Z | |
| dc.date.available | 2026-07-07T08:14:46Z | |
| dc.description | We use an estimate for character sums over finite fields of Katz to solve open problems of Montgomery and Turan. Let h=>2 be an integer. We prove that inf_{|z_k| => 1} max_{v=1,...,n^h} |sum_{k=1}^n z_k^v| <= (h-1+o(1)) sqrt n. This gives the right order of magnitude for the quantity and improves on a bound of Erdos-Renyi by a factor of the order sqrt log n. | |
| dc.description | v1: 9 pages; v2: Minor changes. Fixed error in last three lines of proof of Theorem 2: v3: New title. Minor changes | |
| dc.identifier | https://arxiv.org/abs/0706.4131 | |
| dc.identifier | http://arxiv.org/abs/0706.4131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133245 | |
| dc.subject | Number Theory | |
| dc.subject | 11N30; 11L40 | |
| dc.title | On some power sum problems of Montgomery and Turan | |
| dc.type | text |