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On the Random Character of Fundamental Constant Expansions

Richard E. Crandall
Organization: Center for Advanced Computation
David Bailey
Organization: David Bailey Consultancy
URL: http://www.dbaileyconsultancy.co.uk
Journal / Anthology

Experimental Mathematics
Year: 2001
Volume: 10
Issue: 2
Page range: 175-190

We propose a theory to explain random behavior for the digits in the expansions of fundamental mathematical constants. At the core of our theory is a general hypothesis concerning the distribution of the iterates generated by a certain dynamical map. On this main hypothesis, one obtains proofs of normality (digit randomness in a specific technical sense) for a collection of celebrated constants, including pi, log 2, and others. A connections is drawn between the dynamical model and alternative statistical pictures such as a theory of cascaded pseudorandom number generators. A connection is also established with the theory of irrational and transcendental numbers, leading tot he possibility of normality proofs for number-theoretically motivated entities such as the Erdos-Borwein and Euler constants.

*Mathematics > Number Theory