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Original Articles

On the Random Character of Fundamental Constant Expansions

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Pages 175-190 | Published online: 04 Apr 2012
 

Abstract

We propose a theory to explain random behavior for the digits in the expansions of fundamental mathematical constants. At the core of our approach is a general hypothesis concerning the distribution of the iterates generated by dynamical maps. On this main hypothesis, one obtains proofs of base-2 normality—namely bit randomness in a specific technical sense—for a collection of celebrated constants, including π, log 2, ζ(3), and others. Also on the hypothesis, the number ζ(5) is either rational or normal to base 2. We indicate a research connection between our dynamical model and the theory of pseudorandom number generators.

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