关于有界系数单位的线性组合和双基数展开。

Pub Date : 2013-01-01 Epub Date: 2012-10-06 DOI:10.1007/s00605-012-0443-4

Daniel Krenn, Jörg Thuswaldner, Volker Ziegler

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引用次数: 0

摘要

设[式：见正文]是一个数域的最大阶。贝尔彻在 20 世纪 70 年代证明，如果单位方程[公式：见正文]有一个非难解[公式：见正文]，那么[公式：见正文]中的每一个代数整数都是一对不同单位的和。我们概括了这一结果，并给出了有符号的两位数展开式的应用。

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On linear combinations of units with bounded coefficients and double-base digit expansions.

Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.

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