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On Salem half-norms
Quaestiones Mathematicae ( IF 0.6 ) Pub Date : 2020-12-02 , DOI: 10.2989/16073606.2020.1848938 Toufik Zaïmi 1
中文翻译:
塞勒姆半范数
更新日期:2020-12-02
Quaestiones Mathematicae ( IF 0.6 ) Pub Date : 2020-12-02 , DOI: 10.2989/16073606.2020.1848938 Toufik Zaïmi 1
Affiliation
Abstract
Let α be a Salem number with conjugates , where α1 := α. We prove some properties of the products of the form α1α2 · · · αn, called, by A. Dubickas and C.J. Smyth, Salem half-norms. This allows us to complete, partially, two related results due to C. Christopoulos and J. McKee about the Galois group of the splitting field of the minimal polynomial of α, and to A. Dubickas on a question of D.W. Boyd about Salem numbers which are Mahler measures of non-reciprocal algebraic integers.
中文翻译:
塞勒姆半范数
摘要
令α为带有共轭的 Salem 数,其中α 1 := α。我们证明了α 1 α 2 · · · α n形式的乘积的一些性质,被 A. Dubickas 和 CJ Smyth, Salem 半范数称为。这使我们能够部分完成两个相关的结果,由于 C. Christopoulos 和 J. McKee 关于α的最小多项式的分裂域的 Galois 群,以及 A. Dubickas 关于 DW Boyd 关于 Salem 数的问题是非倒数代数整数的马勒测度。