Liouville Random functions and normal sets
| dc.creator | Fish, Alexander | |
| dc.date | 2005-09-14 | |
| dc.date.accessioned | 2026-07-07T05:23:12Z | |
| dc.date.available | 2026-07-07T05:23:12Z | |
| dc.description | We define a random Liouville function (λ_Q) which depends on a random set (Q) of primes and prove that (A_Q = \{n \in \mathbb{N} | λ_Q(n) = -1 \}) is normal almost everywhere. This fact enables us to generate a family of normal sets such that the equation (xy =z) is not solvable inside them. Additionally we prove that equations (xy=z^2, x^2 + y^2 = square, x^2 - y^2 = square) are solvable in any normal set and for any equation (xy=cn^2) ((c > 1 ), is not a square) there exists a normal set (A_c) such that the equation is not solvable inside (A_c). | |
| dc.description | 6 pages, to appear in Acta Arithmetica | |
| dc.identifier | https://arxiv.org/abs/math/0509315 | |
| dc.identifier | http://arxiv.org/abs/math/0509315 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76341 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11N64; 05D10 | |
| dc.title | Liouville Random functions and normal sets | |
| dc.type | text |