IJPAM: Volume 64, No. 2 (2010)

GENERALIZED REDÉI RATIONAL FUNCTIONS AND
RATIONAL APPROXIMATIONS OVER CONICS

Stefano Barbero$^1$, Umberto Cerruti$^2$, Nadir Murru$^3$
$^{1,2,3}$Department of Mathematics
University of Turin
10, Via Carlo Alberto, Turin, 10123, ITALY
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


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. Further more, 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.

Received: August 12, 2010

AMS Subject Classification: 11B39, 11D09, 11J68

Key Words and Phrases: continued fractions, groups over conics, quadratic irrationalities, rational approximations, Redéi rational functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 2