Leopoldt’s conjecture in parameterized families
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- by Johannes Buchmann and Jonathan W. Sands PDF
- Proc. Amer. Math. Soc. 104 (1988), 43-48 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 43-48
- MSC: Primary 11R27; Secondary 11R37
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958040-4
- MathSciNet review: 958040