On the Normality of Arithmetical Constants

Details On the Normality of Arithmetical Constants On the Normality of Arithmetical Constants

2001-01-08

arxiv.org/abs/math/0101055v2

Experimental Mathematics 10, no. 3 (2001), 355--368

Mathematics

Number Theory

Revised final version, February 2001, 21 pages, latex; small corrections

Scientific paper

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.

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