On the Random Character of Fundamental Constant Expansions

2001/01/01 by David H. Bailey, Richard E. Crandall · 3 citations
Computer Science · Mathematics · #Algorithm #Base (topology) #Benford’s Law and Fraud Detection #Chaos-based Image/Signal Encryption #Character (mathematics) #Computability, Logic, AI Algorithms #Computer science #Connection (principal bundle) #Constant (computer programming) #Discrete mathematics #Iterated function #Mathematical analysis #Mathematical proof #Mathematics #Normality #Pseudorandom number generator #Pseudorandomness #Randomness #Statistics

paper · pdf · doi:10.1080/10586458.2001.10504441

openalex publication_date 2001/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• Computational strategies for the Riemann zeta function
• Analysis of PSLQ, an integer relation finding algorithm
• On a problem of Steinhaus about normal numbers
• Note on normal numbers
• The Construction of Decimals Normal in the Scale of Ten
• On the rapid computation of various polylogarithmic constants
• Random Generators and Normal Numbers
• Absolutely Abnormal Numbers

Cited by

• Random Generators and Normal Numbers
• An example of a computable absolutely normal number
• Normal number [wikipedia]