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- W2193117963 abstract "Let P(K) be the set of Pisot numbers generating a real algebraic number field K over the field of rationals Q. Then, a result of Meyer implies that P(K) is relatively dense in the interval [1,∞) and a theorem of Pisot gives that P(K) contains units, whenever K≠Q. In the present note, we prove analogous results for the set of complex Pisot numbers generating a non-real number field K′ over Q when K′ is neither a quadratic field nor a CM-field. Soient K un corps réel de nombres algébriques et P(K) l'ensemble des nombres de Pisot engendrant K sur le corps des rationnels Q. Un résultat, dû à Meyer, montre que P(K) est relativement dense dans l'intervalle [1,∞), et un théorème de Pisot établit que l'ensemble P(K) contient des unités lorsque K≠Q. On considère, dans cette note, un corps non réel K′ de nombres algébriques, et l'on obtient des résultats similaires aux précédents pour l'ensemble des nombres de Pisot complexes engendrant K′ sur Q lorsque K′ n'est, ni un corps quadratique, ni un corps CM." @default.
- W2193117963 created "2016-06-24" @default.
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- W2193117963 date "2015-11-01" @default.
- W2193117963 modified "2023-10-02" @default.
- W2193117963 title "Complex Pisot numbers in algebraic number fields" @default.
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- W2193117963 doi "https://doi.org/10.1016/j.crma.2015.09.007" @default.
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