Multi-quadratic p-rational number fields

For each odd prime p, we prove the existence of infinitely many real quadratic fields which are p-rational. Explicit imaginary and real bi-quadratic p-rational fields are also given for each prime p. Using a recent method developed by Greenberg, we deduce the existence of Galois extensions of Q with...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 225; no. 9; p. 106657
Main Authors Benmerieme, Y., Movahhedi, A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2021
Elsevier
Subjects
Galois representation
Mathematics
p-rational number field
secondary
p-rational number field
Galois representation
Primary
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Summary:For each odd prime p, we prove the existence of infinitely many real quadratic fields which are p-rational. Explicit imaginary and real bi-quadratic p-rational fields are also given for each prime p. Using a recent method developed by Greenberg, we deduce the existence of Galois extensions of Q with Galois group isomorphic to an open subgroup of GLn(Zp), for n=4 and n=5 and at least for all the primes p<192.699.943.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2020.106657