Experimental Mathematics

On the Random Character of Fundamental Constant Expansions

David H. Bailey and Richard E. Crandall

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.

Article information

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

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.em/999188630

Mathematical Reviews number (MathSciNet)
MR1837669

Zentralblatt MATH identifier
1047.11073

Citation

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


Export citation