On some cubic or quartic algebraic units |
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Authors: | Stéphane Louboutin |
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Institution: | Institut de Mathematiques de Luminy, Marseille Cedex 9, France |
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Abstract: | Let ? be an algebraic unit such that rank of the unit group of the order Z?] is equal to one. It is natural to ask whether ? is a fundamental unit of this order. To prove this result, we showed that it suffices to find explicit positive constants c1, c2 and c3 such that for any such ? it holds that c1c2|?|?d??c3|?|2c2, where d? denotes the absolute value of the discriminant of ?, i.e. of the discriminant of its minimal polynomial. We give a proof of this result, simpler than the original ones. |
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Keywords: | primary 11R27 secondary 11R16 11R09 |
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