Continued fractions for hyperquadratic power series over a finite field
Continued fractions for hyperquadratic power series over a finite field
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DOI：
10.1016/j.ffa.2007.01.001
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发表时间：
2008-04
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影响因子：
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通讯作者：
A. Lasjaunias
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文献类型：
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作者：
A. Lasjaunias
特征为p的有限域Fq上的无理幂级数如果满足形式为x=(AXR+B)/(CXR+D)的代数方程x=(AXR+B)/(CXR+D)，则称其为超二次，其中r是p的幂，系数属于Fq[T]。这些代数幂函数级数是二次实数的类似。这种类比使他们的连分式展开式像在经典情况下一样具体，但更复杂。在这里，我们给出了一些此类展开的生成方式的一般结果。我们用它来描述几类具有规则模式的展开式。
An irrational power series over a finite field Fqof 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 Fq[T]. 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.