Principal solutions of recurrence relations and irrationality questions in number theory
| dc.creator | Mingarelli, Angelo B. | |
| dc.date | 2006-08-23 | |
| dc.date | 2008-03-27 | |
| dc.date.accessioned | 2026-07-07T09:28:41Z | |
| dc.date.available | 2026-07-07T09:28:41Z | |
| dc.description | We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, for an irrational number associated with solutions of three-term linear recurrence relations we show that there exists a four-term linear recurrence relation whose solutions allow us to show that the number is a quadratic irrational if and only if the four-term recurrence relation has a principal solution of a certain type. The result is extended to higher order recurrence relations and a transcendence criterion can also be formulated in terms of these principal solutions. When applied to the situation of powers of $ζ(3)$ it is not known whether the corresponding four term recurrence relation does or does not have such a principal solution, however the method does generate new series expansions of powers of $ζ(3)$ and $ζ(2)$ in terms of Apéry's now classic sequences. | |
| dc.description | Revision of previous versions.. | |
| dc.identifier | https://arxiv.org/abs/math/0608577 | |
| dc.identifier | http://arxiv.org/abs/math/0608577 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157513 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 11M06; 11J72; 39A11;39A12 | |
| dc.title | Principal solutions of recurrence relations and irrationality questions in number theory | |
| dc.type | text |