Approximate Squaring
| dc.creator | Lagarias, J. C. | |
| dc.creator | Sloane, N. J. A. | |
| dc.date | 2003-09-23 | |
| dc.date | 2003-12-11 | |
| dc.date.accessioned | 2026-07-07T08:18:14Z | |
| dc.date.available | 2026-07-07T08:18:14Z | |
| dc.description | We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then eventually an integer will be reached. We prove this when d=2, and provide evidence that it is true in general by giving an upper bound on the density of the ``exceptional set'' of numbers which fail to reach an integer. We give similar results for a p-adic analogue of f, when the exceptional set is nonempty, and for iterating the ``approximate multiplication'' map f_r(x) := r ceiling(x) where r is a fixed rational number. | |
| dc.description | 22 pages. Revised Nov 9, 2003: new theorems, including probabilistic interpretation of results, also analogs for floor function (24 pages) | |
| dc.identifier | https://arxiv.org/abs/math/0309389 | |
| dc.identifier | http://arxiv.org/abs/math/0309389 | |
| dc.identifier | Experimental Math. 13 (2004), 113--128. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134363 | |
| dc.subject | Number Theory | |
| dc.subject | Information Theory | |
| dc.subject | Primary 26A18; Secondary 11B83, 11K31, 11Y99 | |
| dc.title | Approximate Squaring | |
| dc.type | text |