Continued fractions for hyperquadratic power series over a finite field |
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Authors: | Alain Lasjaunias |
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Institution: | aC.N.R.S.-UMR 5465, Université Bordeaux I, Talence 33405, France |
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Abstract: | An irrational power series over a finite field of characteristic p is called hyperquadratic if it satisfies an algebraic equation of the form x=(Axr+B)/(Cxr+D), where r is a power of p and the coefficients belong to . These algebraic power series are analogues of quadratic real numbers. This analogy makes their continued fraction expansions specific as in the classical case, but more sophisticated. Here we present a general result on the way some of these expansions are generated. We apply it to describe several families of expansions having a regular pattern. |
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Keywords: | Finite fields Fields of power series Continued fractions |
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