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Groupe des unités pour des extensions diédrales complexes de degré 10 sur Q

Omar Kihel (2001)

Journal de théorie des nombres de Bordeaux

Le but de cet article est de montrer qu’un ensemble quelconque de quatre racines des polynômes quintiques p ( x ) exhibés par H . Darmon forme sous certaines conditions un système fondamental d’unités de la fermeture normale du corps 𝐐 ( θ ) p ( θ ) = 0 .

Haar system on a product of zero-dimensional compact groups

Sergei Lukomskii (2011)

Open Mathematics

In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.

Halfway to a solution of X 2 - D Y 2 = - 3

R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)

Journal de théorie des nombres de Bordeaux

It is well known that the continued fraction expansion of D readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of x 2 - D y 2 = ± 1 . Here we notice that, analogously, the point halfway to a solution of x 2 - D y 2 = - 3 can be recognised. We explain what is going on.

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