NATURAL EXTENSION METHOD FOR TEH ERGODIC THOERY OF NUMBER THEORETIC TRANSFORMATIONS

数论变换遍历理论的自然推广方法

基本信息

批准号：
09640220
负责人：
NAKADA Hitoshi
金额：
$ 1.92万
依托单位：
KEIO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640220/
关键词：
ERGODIC THEORY NUMBER THEORETIC TRANSFORMATION CONTINUED FRACTIONS 自然拡大正規数

项目摘要

1. Normal numbers of Number theoretic transformations We showed that the set of regular continued fraction normal numbers is identical with the set of the nearest integer continued fraction normal numbers. We also gave a definition of B-normal numbers and showed that the set of those numbers includes the set of regular c.f. normal numbers. We appliied the proof of these results to the normal number problem proposed by F.Schweiger. We gave a negative answer on this problem.2. We considered backward continued fractions transformations associated to Hecke groups and constructed their natural extensions. As a result, we gave characterizations of hyperbolic points and elliptic points of Hecke groups by the periodicity and the finiteness of the c.f. expansions. It turned out that these are natural generalizations of the backward continued fractions for real numbers.3. We extended the notion of number theoretic transformations to non-archimedian fields. First we consider continued fractions over the set of formal Laurent power seris with a finite field coefficients. Here the continued fraction digits are polynomials with the finite field coefficients. Next, we started to study f-expansion theory in this case and we will continue for some years on this problem. Main part of the project will be to study the theory of Fibered Systems fornon- archimedian fileds.

1。数字理论转换的正常数量，我们表明，常规持续分数正常数的集合与最近的整数持续分数正常数相同。我们还给出了B正常数的定义，并表明这些数字的集合包括一组常规C.F.正常数字。我们将这些结果的证明应用于F.Schweiger提出的正常数量问题。我们对这个问题给出了负面答案。2。我们考虑了与Hecke组相关的持续持续分数转换，并构建了它们的自然扩展。结果，我们根据C.F.的周期性和有限性给出了Hecke组双曲点和椭圆点的特征。扩展。事实证明，这些是实际数字的向后持续部分的自然概括。3。我们将数字理论转换的概念扩展到了非Archimedian字段。首先，我们考虑具有有限场系数的正式朗朗力量Seris组合的持续分数。在这里，持续的分数数字是具有有限场系数的多项式。接下来，在这种情况下，我们开始研究F-膨胀理论，我们将在这个问题上继续多年。该项目的主要部分将是研究纤维系统的理论，即诉讼。