English

Normal integral bases of Lehmer's cyclic quintic fields

Number Theory 2024-04-15 v4

Abstract

Let KnK_n be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for KnK_n only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that n4+5n3+15n2+25n+25n^4+5n^3+15n^2+25n+25 is prime number, and Spearman-Willliams in the case that n4+5n3+15n2+25n+25n^4+5n^3+15n^2+25n+25 is square-free.

Keywords

Cite

@article{arxiv.2209.10858,
  title  = {Normal integral bases of Lehmer's cyclic quintic fields},
  author = {Yu Hashimoto and Miho Aoki},
  journal= {arXiv preprint arXiv:2209.10858},
  year   = {2024}
}