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Distribution of quadratic non-residues which are not primitive roots

S. Gun, B. Ramakrishnan, Binod Kumar Sahoo, Ravindranathan Thangadurai (2005)

Mathematica Bohemica

In this article we study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo p h or 2 p h for an odd prime p and h ≥ 1 an integer.

Divisibilité par 19

Badoureau (1879)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Dyadic diaphony of digital sequences

Friedrich Pillichshammer (2007)

Journal de Théorie des Nombres de Bordeaux

The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital ( 0 , s ) -sequences over ℤ 2 , s = 1 , 2 . These formulae show that for fixed s ∈ { 1 , 2 } , the dyadic diaphony has the same values for any digital ( 0 , s ) -sequence. For s = 1 , it follows that the dyadic diaphony and the diaphony of special digital ( 0 , 1 ) -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital...

Dynamical directions in numeration

Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner (2006)

Annales de l’institut Fourier

This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to β -numeration and its generalisations, abstract numeration systems and...

Dynamique des nombres et physique des oscillateurs

Jacky Cresson (2008)

Journal de Théorie des Nombres de Bordeaux

Nous présentons un modèle mathématique permettant de reproduire le spectre expérimental des fréquences dans un composant électronique appelé boucle ouverte. Le spectre semble s’organiser suivant une contrainte de nature diophantienne sur les fréquences. Sa structure peut donc se comprendre via une étude de l’ensemble des fractions continues en fonction de leur longueur et de la taille des quotients partiels.

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