On the non-randomness of modular arthmetic progressions : a solution to a problem by V.I. Arnold

Eda Cesaratto (1) , Alain Plagne (2) , Brigitte Vallée (1)

1 Equipe AMACC - Laboratoire GREYC - UMR6072
2 CMLS - Centre de Mathématiques Laurent Schwartz

We solve a problem by V. I. Arnold dealing with “how random” modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form in the case of arithmetic progressions. This simplified expression is then estimated using the methodology of dynamical analysis, which operates with tools coming from dynamical systems theory.

Domaines: Algorithme et structure de données [cs.DS]

Eda Cesaratto, Alain Plagne, Brigitte Vallée. On the non-randomness of modular arthmetic progressions : a solution to a problem by V.I. Arnold. 2008. ⟨hal-00211041⟩