Almost Alternating Sums
| dc.creator | O'Bryant, Kevin | |
| dc.creator | Reznick, Bruce | |
| dc.creator | Serbinowska, Monika | |
| dc.date | 2003-08-09 | |
| dc.date | 2005-08-24 | |
| dc.date.accessioned | 2026-07-07T06:34:15Z | |
| dc.date.available | 2026-07-07T06:34:15Z | |
| dc.description | Writing for a general mathematical audience, we provide elementary upper and lower bounds on the growth (as a function of N) of the sum \sum_{n=1}^N (-1)^{\floor{n x}} for various fixed x. For example, if x is a quadratic irrational, then the sum is O(log N), and if x is 2/(e-1), then the sum is O(log N / log log N). We compute the optimal big-Oh constant for x=\sqrt{2}, 1+\sqrt{5}, 2+\sqrt{10}, .... | |
| dc.description | 17 pages, 3 figures (revision is typographical) | |
| dc.identifier | https://arxiv.org/abs/math/0308087 | |
| dc.identifier | http://arxiv.org/abs/math/0308087 | |
| dc.identifier | Amer. Math. Monthly 113 (2006), no. 8, 673--688. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99469 | |
| dc.subject | Number Theory | |
| dc.subject | 11K06 (Primary), 11J70 (Secondary) | |
| dc.title | Almost Alternating Sums | |
| dc.type | text |