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arXiv · 2209.10858

Normal integral bases of Lehmer's cyclic quintic fields

Yu Hashimoto·Miho Aoki
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Abstract

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

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Yu Hashimoto, Miho Aoki. 2022-09-22. Normal integral bases of Lehmer's cyclic quintic fields. https://arxiv.org/abs/2209.10858

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