Arithmetic properties of 3-cycles of quadratic maps over Q
| dc.contributor.author | Morton, Patrick | |
| dc.contributor.author | Raianu, Serban | |
| dc.contributor.department | Mathematical Sciences, School of Science | |
| dc.date.accessioned | 2023-11-01T18:57:46Z | |
| dc.date.available | 2023-11-01T18:57:46Z | |
| dc.date.issued | 2022-11 | |
| dc.description.abstract | It is shown that c = -29/16 is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map fc(x) = x2 + c has a rational periodic point of period 3. Several arithmetic conditions on the set of all such rational numbers c and the rational orbits of fc(x) are proved. A graph on the numerators of the rational 3-periodic points of maps fc is considered which reflects connections between solutions of norm equations from the cubic field of discriminant -23. | |
| dc.eprint.version | Author's manuscript | |
| dc.identifier.citation | Morton, P., & Raianu, S. (2022). Arithmetic properties of 3-cycles of quadratic maps over Q. Journal of Number Theory, 240, 685–729. https://doi.org/10.1016/j.jnt.2022.01.005 | |
| dc.identifier.uri | https://hdl.handle.net/1805/36851 | |
| dc.language.iso | en_US | |
| dc.publisher | Elsevier | |
| dc.relation.isversionof | 10.1016/j.jnt.2022.01.005 | |
| dc.relation.journal | Journal of Number Theory | |
| dc.rights | Publisher Policy | |
| dc.source | ArXiv | |
| dc.subject | arithmetic properties | |
| dc.subject | quadratic map | |
| dc.subject | periodic points | |
| dc.subject | rational orbits | |
| dc.subject | rational numbers | |
| dc.title | Arithmetic properties of 3-cycles of quadratic maps over Q | |
| dc.type | Article |