Leopoldt's conjecture in parameterized families

Johannes Buchmann, Jonathan W. Sands
1988 Proceedings of the American Mathematical Society  
For each fixed prime p ^ 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 ¿55. 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.
doi:10.1090/s0002-9939-1988-0958040-4 fatcat:ohtvnu3lfjgjrlvf26tk2wy2da