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Good’s theorem for Hurwitz continued fractions
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-02-20 , DOI: 10.1142/s1793042120500761
Gerardo Gonzalez Robert 1
Affiliation  

Good’s Theorem for regular continued fraction states that the set of real numbers [Formula: see text] such that [Formula: see text] has Hausdorff dimension [Formula: see text]. We show an analogous result for the complex plane and Hurwitz Continued Fractions: the set of complex numbers whose Hurwitz Continued fraction [Formula: see text] satisfies [Formula: see text] has Hausdorff dimension [Formula: see text], half of the ambient space’s dimension.

中文翻译:

赫尔维茨连分数的古德定理

正则连分数的古德定理指出实数集 [公式:见正文] 使得 [公式:见正文] 具有豪斯多夫维数 [公式:见正文]。我们展示了复平面和 Hurwitz 连分数的类似结果:复数的集合,其 Hurwitz 连分数 [公式:见文本] 满足 [公式:见文本] 具有 Hausdorff 维数 [公式:见文本],环境的一半空间的维度。
更新日期:2020-02-20
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