On the Normality of Arithmetical Constants
Number Theory
2007-05-23 v2 Dynamical Systems
Abstract
D. Bailey and R. E. Crandall recently formulated a "Hypothesis A", which provides a general principle to explain the (conjectured) normality of constants like pi or log 2 and other related numbers, to base 2 or other integer bases. This paper explains the basic mechanism behind their principle as a connection between single orbits of two different discrete dynamical systems. It relates a subclass of arithmetical constants they consider to special values of G-functions, and characterizes this subclass. Finally it notes some parallels of "Hypothesis A" with Furstenberg's conjecture on invariant measures.
Cite
@article{arxiv.math/0101055,
title = {On the Normality of Arithmetical Constants},
author = {Jeffrey C. Lagarias},
journal= {arXiv preprint arXiv:math/0101055},
year = {2007}
}
Comments
Revised final version, February 2001, 21 pages, latex; small corrections