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Leopoldt's conjecture in parameterized families

Authors: Johannes Buchmann and Jonathan W. Sands
Journal: Proc. Amer. Math. Soc. 104 (1988), 43-48
MSC: Primary 11R27; Secondary 11R37
MathSciNet review: 958040
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Abstract: For each fixed prime $ p \ne 5$, we prove Leopoldt's conjecture in two infinite families of fields of degree five whose normal closure has Galois group over the rationals isomorphic to $ {S_5}$. The units of these fields were determined by Maus [4]; we develop and apply a simple reformulation of Leopoldt's conjecture to obtain the result. We also observe that Leopoldt's conjecture in one field can imply the same in a second field related by congruence conditions.

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