In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Pad´e approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, R´edei rational functions are introduced as convergents of particular periodic continued fractions and are applied for approximating square roots in the field of p-adic numbers and to study periodic representations. Using the results over the real numbers, we show how to construct periodic continued fractions and approximations of square roots which are simultaneously valid in the real and in the p-adic field.

Periodic representations and rational approximations of square roots

CERRUTI, Umberto;MURRU, NADIR
2013-01-01

Abstract

In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Pad´e approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, R´edei rational functions are introduced as convergents of particular periodic continued fractions and are applied for approximating square roots in the field of p-adic numbers and to study periodic representations. Using the results over the real numbers, we show how to construct periodic continued fractions and approximations of square roots which are simultaneously valid in the real and in the p-adic field.
175
Novembre 2013
83
90
http://arxiv.org/abs/1409.6159v1
Continued fraction; Diophantine approximation; Newton approximation; Padé approximation; Rédei rational function; p-adic numbers
Marco Abrate; 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/2318/136802
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