Research Article
Normal integral bases of Lehmer's cyclic quintic fields
https://doi.org/10.21203/rs.3.rs-2593630/v1
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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
normal integral basis
cyclic quintic field
Gaussian period
tamely ramified extension
No competing interests reported.
Reviews received at journal
02 Mar, 2024
Reviewers agreed at journal
02 Mar, 2024
Reviewers agreed at journal
06 Mar, 2023
Reviewers invited by journal
24 Feb, 2023
Editor assigned by journal
21 Feb, 2023
Submission checks completed at journal
18 Feb, 2023
First submitted to journal
16 Feb, 2023
You are reading this latest preprint version