Normal integral bases of  Lehmer's cyclic quintic fields

Abstract

Let Kn be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for Kn only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that n4+5n3+15n2+25n+25 is prime number, and Spearman-Willliams in the case that n4+5n3+15n2+25n+25 is square-free. Mathematics Subject Classification (2010) Primary 11R04 · 11R20, Secondary 11C08 · 11L05 · 11R80