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2001 On the Random Character of Fundamental Constant Expansions
David H. Bailey, Richard E. Crandall
Experiment. Math. 10(2): 175-190 (2001).


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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David H. Bailey. Richard E. Crandall. "On the Random Character of Fundamental Constant Expansions." Experiment. Math. 10 (2) 175 - 190, 2001.


Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 1047.11073
MathSciNet: MR1837669

Rights: Copyright © 2001 A K Peters, Ltd.


Vol.10 • No. 2 • 2001
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