的续分扩展周期长度的第一和第二矩

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-07-23 DOI:10.1112/mtk.12273

Francesco Battistoni, Loïc Grenié, Giuseppe Molteni

引用次数: 0

摘要

设为任意正整数和非平方整数。我们证明了...的续分数展开周期长度的前两个矩的上界。这样就可以改进现有的关于 .

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The first and second moments for the length of the period of the continued fraction expansion for

Let be any positive and non-square integer. We prove an upper bound for the first two moments of the length of the period of the continued fraction expansion for . This allows to improve the existing results for the large deviations of .

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.