Nombre de classes, unités et bases d’entiers des extensions cubiques cycliques de
Nombres de Pisot et fonctions moyenne-périodiques
Non-monogenity of multiquadratic number fields
Non-Wieferich primes in number fields and -conjecture
Let be an algebraic number field of class number one and let be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in under the assumption of the -conjecture for number fields.
Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics
Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.
Normal integral bases for infinite abelian extensions
Normal orders for certain functions associated with factorizations in number fields
Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis
Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminantA large part of the proof is in establishing the following more general result: Let be a Galois number field of odd prime degree and conductor . Assume the GRH for . Ifthen is not norm-Euclidean.
Norms in finite Galois extensions of the rationals.
Number fields with the same index