Continued Fractions for Algebraic Formal Power Series over a Finite Base Field
نویسندگان
چکیده
منابع مشابه
On Continued Fractions over the Field of Formal Power Series
This paper dealt with by studying continued fractions of the form c 1 1 + c 1 1 + · · · + c 1 1 + · · · Necessary and sufficient conditions are given for a sequence of it to be convergent in the formal powers series case.
متن کاملSpecialisation and Reduction of Continued Fractions of Formal Power Series
We discuss and illustrate the behaviour of the continued fraction expansion of a formal power series under specialisation of parameters or their reduction modulo p and sketch some applications of the reduction theorem here proved.
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We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
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We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملInvariance principles for Diophantine approximation of formal Laurent series over a finite base field
In a recent paper, the first and third author proved a central limit theorem for the number of coprime solutions of the diophantine approximation problem for formal Laurent series in the setting of the classical theorem of Khintchine. In this note, we consider a more general setting and show that even an invariance principle holds, thereby improving upon earlier work of the second author. Our r...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1999
ISSN: 1071-5797
DOI: 10.1006/ffta.1998.0236