四次塞勒姆数是非倒数2-皮索数的马勒测度

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-01-08 DOI:10.5802/JTNB.1145

Toufik Zaïmi

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引用次数: 1

摘要

在M. J. Bertin问题的激励下，我们得到了四次Salem数的最小多项式的参数化，如α，它是非互反2-Pisot数的Mahler测度。这允许我们用给定的迹来确定所有这样的数α，并推导出对于任何自然数t (p。t≥2时，轨迹t有一个四次塞勒姆数，即(p。它不是非倒数2-皮索数的马勒测度。

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Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers

Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say α, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers α with a given trace, and to deduce that for any natural number t (resp. t ≥ 2) there is a quartic Salem number of trace t which is (resp. which is not) a Mahler measure of a non-reciprocal 2-Pisot number.

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来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).