In this paper we study a general class of conics starting from a quotient field. We give a group structure over these conics generalizing the construction of a group over the Pell hyperbola. Furthermore, we generalize the definition of Redéi rational functions in order to use them for evaluating powers of points over these conics. Finally, we study rational approximations of irrational numbers over conics, obtaining a new result for the approximation of quadratic irrationalities.

Generalized Rédei rational functions and rational approximations over conics

CERRUTI, Umberto;MURRU, NADIR
2010-01-01

Abstract

In this paper we study a general class of conics starting from a quotient field. We give a group structure over these conics generalizing the construction of a group over the Pell hyperbola. Furthermore, we generalize the definition of Redéi rational functions in order to use them for evaluating powers of points over these conics. Finally, we study rational approximations of irrational numbers over conics, obtaining a new result for the approximation of quadratic irrationalities.
64
305
316
http://arxiv.org/pdf/1209.0573.pdf
http://math.uctm.edu/journals/contents/2010-64-2/index.html
continued fractions; groups iver conics; quadratic irrationalities; rational approximations; Rédei rational functions
Stefano Barbero; Umberto Cerruti; Nadir Murru
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/78800
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