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Lagarias, Jeffrey C.

On the normality of arithmetical constants. (English) Zbl 1015.11036

Exp. Math. 10, No. 3, 355-368 (2001).
This paper shows that there is a basic mechanism underlying a principle introduced by D. H. Baily and R. E. Crandall [Exp. Math. 10, 175-190 (2001)] and formulated by them as Hypothesis A in order to explain the (conjectured) normality of the binary expansion of constants like \(\pi\) and other related numbers. The paper also points out an analogy of Hypothesis A with Furstenberg’s conjecture on invariant measures.
Reviewer: L.Heinrich (Augsburg)

Cited in 3 Documents

MSC:

11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
11A63 Radix representation; digital problems
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)

Keywords:

normal numbers; beta-expansions; binary expansion; Furstenberg’s conjecture; invariant measures
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