Multi-quadratic p-rational Number Fields

2020/07/09 by Benmerieme, Youssef, Movahhedi, Abbas
#11R23 #11R32 #11R42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2007.04864

Abstract

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 GL_n(Z_p), for n =4 and n =5 and at least for all the primes p <192.699.943.

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