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On the Normality of Arithmetical Constants

Jeffrey C. Lagarias
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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.

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Jeffrey C. Lagarias. 2002-08-25. On the Normality of Arithmetical Constants. https://arxiv.org/abs/math/0101055

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