Lower bounds on the projective heights of algebraic points
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we...
Monogénéité de l'anneau des entiers de certains corps de classes de rayon
Soient une extension quadratique imaginaire de et son anneau des entiers. Lorsque 3 est décomposé dans , nous démontrons que les anneaux d’entiers de certains corps de classe de rayon de sont monogènes sur l’anneau des entiers du corps de classes de rayon 3. Des générateurs de “monogénéite” sont obtenus a l’aide de fonctions elliptiques qui paramétrisent un modèle de Deuring de la courbe elliptique associée au réseau .
Monogénéité de l'anneau des entiers de corps de classes de rayon de corps quadratiques
Monogénéité de l'anneau des entiers des extensions cycliques imaginaries de degré 2 l (l premier ... 5).
Multiplicative dependence of shifted algebraic numbers
We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.
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
O devátém Hilbertově problému
O rozšíření pojmu kongruence
Okutsu invariants and Newton polygons
On a certain additive function on the Gaussian integers