Artículo
Markoff-Rosenberger triples in arithmetic progression
Autor/es | González Jiménez, Enrique
Tornero Sánchez, José María |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2013-06 |
Fecha de depósito | 2016-06-07 |
Publicado en |
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Resumen | We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in ... We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x 2 +y 2 +z 2 = dxyz over quadratic fields and the classic Markoff equation x 2 + y 2 + z 2 = 3xyz over an arbitrary number field. |
Identificador del proyecto | MTM2009–07291
FQM–218 P08–FQM–03894 |
Cita | González Jiménez, E. y Tornero Sánchez, J.M. (2013). Markoff-Rosenberger triples in arithmetic progression. Journal of Symbolic Computation, 53, 53-63. |
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