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Salem number : ウィキペディア英語版 | Salem number In mathematics, a Salem number is a real algebraic integer ''α'' > 1 whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem. == Properties ==
Because it has a root of absolute value 1, the minimal polynomial for a Salem number must be reciprocal. This implies that 1/''α'' is also a root, and that all other roots have absolute value exactly one. As a consequence α must be a unit in the ring of algebraic integers, being of norm 1. Every Salem number is a Perron number (a real algebraic number greater than one all of whose conjugates have smaller absolute value).
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Salem number」の詳細全文を読む
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