Experimental Mathematics

On the Random Character of Fundamental Constant Expansions

David H. Bailey and Richard E. Crandall


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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Experiment. Math. Volume 10, Issue 2 (2001), 175-190.

First available in Project Euclid: 30 August 2001

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Bailey, David H.; Crandall, Richard E. On the Random Character of Fundamental Constant Expansions. Experiment. Math. 10 (2001), no. 2, 175--190. http://projecteuclid.org/euclid.em/999188630.

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