具有任意长周期的超椭圆场中的连续分数

Pub Date : 2024-05-13 DOI:10.1134/S1064562424701928

V. P. Platonov, G. V. Fedorov

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引用次数: 0

摘要

摘要文章证明了以下陈述：在代数数域 K 上定义的任何超椭圆域 L 中，如果域 L 的整数元素环上有非三维单元，则存在一个元素，其续分数的周期长度大于任何给定的数。

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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Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period

The article proves the following statement: in any hyperelliptic field L defined over the field of algebraic numbers K which having non-trivial units of the ring of integer elements of the field L, there is an element for which the period length of the continued fraction is greater any pre-given number.

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