Uncomputably Large Integral Points on Algebraic Plane Curves?
| dc.creator | Rojas, J. Maurice | |
| dc.date | 1998-09-02 | |
| dc.date.accessioned | 2026-07-07T05:25:52Z | |
| dc.date.available | 2026-07-07T05:25:52Z | |
| dc.description | We show that the decidability of an amplification of Hilbert's Tenth Problem in three variables implies the existence of uncomputably large integral points on certain algebraic curves. We obtain this as a corollary of a new positive complexity result: the Diophantine prefixes EAE and EEAE are generically decidable. This means, taking the former prefix as an example, that we give a precise geometric classification of those polynomials f in Z[v,x,y] for which the question... ``Does there exists a v in N such that for all x in N, there exists a y in N with f(v,x,y)=0?'' ...may be undecidable, and we show that this set of polynomials is quite small in a rigourous sense. (The decidability of EAE was previously an open question.) The analogous result for the prefix EEAE is even stronger. We thus obtain a connection between the decidability of certain Diophantine problems, height bounds for points on curves, and the geometry of certain complex surfaces and 3-folds. | |
| dc.identifier | https://arxiv.org/abs/math/9809009 | |
| dc.identifier | http://arxiv.org/abs/math/9809009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77346 | |
| dc.subject | Number Theory | |
| dc.subject | Computational Complexity | |
| dc.subject | Symbolic Computation | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Logic | |
| dc.subject | 03D35, 11D72, 14G99; 11G30, 14H99, 14J26 | |
| dc.title | Uncomputably Large Integral Points on Algebraic Plane Curves? | |
| dc.type | text |