论文标题
P-ADIC持续分数的新算法
A new algorithm for p-adic continued fractions
论文作者
论文摘要
$ P $领域的持续分数 - 几位作者最近研究了ADIC数字。众所周知，正二次非理性的实际持续部分最终是周期性的（Lagrange定理）。仍然不知道是否存在具有类似属性的ADIC持续分数算法。在本文中，我们修改并改善了Browkin的一种算法。目前，该算法被认为是最好的算法之一。我们的新算法显示出更好的周期性特性。我们为整数的平方根展示，如果我们的算法产生定期扩展，那么这种周期性扩展将有一个前一个。从实验上看来，我们的算法比Browkin的算法产生的二次非理性的持续分数更多。因此，它更接近了Lagrange定理的类似物的算法。
Continued fractions in the field of $p$--adic numbers have been recently studied by several authors. It is known that the real continued fraction of a positive quadratic irrational is eventually periodic (Lagrange's Theorem). It is still not known if a $p$--adic continued fraction algorithm exists that shares a similar property. In this paper we modify and improve one of Browkin's algorithms. This algorithm is considered one of the best at the present time. Our new algorithm shows better properties of periodicity. We show for the square root of integers that if our algorithm produces a periodic expansion, then this periodic expansion will have pre-period one. It appears experimentally that our algorithm produces more periodic continued fractions for quadratic irrationals than Browkin's algorithm. Hence, it is closer to an algorithm to which an analogue of Lagrange's Theorem would apply.
