Hilbert-Speiser number fields for a prime p inside the p-cyclotomic field |
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Authors: | Humio Ichimura |
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Affiliation: | Faculty of Science, Ibaraki University, Bunkyo 2-1-1, Mito, 310-8512, Japan |
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Abstract: | Let p be a prime number. We say that a number field F satisfies the condition when for any cyclic extension N/F of degree p, the ring of p-integers of N has a normal integral basis over . It is known that F=Q satisfies for any p. It is also known that when p?19, any subfield F of Q(ζp) satisfies . In this paper, we prove that when p?23, an imaginary subfield F of Q(ζp) satisfies if and only if and p=43, 67 or 163 (under GRH). For a real subfield F of Q(ζp) with F≠Q, we give a corresponding but weaker assertion to the effect that it quite rarely satisfies . |
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Keywords: | 11R18 11R33 11R23 |
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