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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0958040-4
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.


References [Enhancements On Off] (What's this?)

  • [1] A. Brumer, On the units of algebraic number fields, Mathematika 14 (1967), 121-124. MR 0220694 (36:3746)
  • [2] J. Buchmann and J. W. Sands, An algorithm for testing Leopoldt's conjecture, J. Number Theory 27 (1987), 92-105. MR 904010 (88m:11090)
  • [3] R. Gillard, Formulations de la conjecture de Leopoldt et étude d'une condition suffisante, Abh. Math. Sem. Univ. Hamburg 48 (1979), 125-138. MR 537453 (80i:12007)
  • [4] E. Maus, Zur Arithmetik einiger Serien nichtauflösbarer Gleichungen 5. Grades, Abh. Math. Sem. Univ. Hamburg 54 (1984), 227-250. MR 780251 (86g:12006)
  • [5] T. Nguyen-Quang-Do, Sur la structure Galoisienne des corps locaux et la théorie d'Iwasawa, Comp. Math. 46 (1982), 85-119. MR 660155 (84j:12016a)
  • [6] J.-P. Serre, Sur le résidue de la fonction zêta $ p$-adique d'une corps de nombres, C.R. Acad. Sci. Paris 287 (1978), 183-188. MR 0506177 (58:22024)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0958040-4
Article copyright: © Copyright 1988 American Mathematical Society

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