A Strong Hot Spot Theorem
Journal Article
·
· Proceedings of the American Mathematical Society
OSTI ID:886604
A real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it possesses no base-b ''hot spot''. In other words, alpha is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of alpha with larger and larger frequencies, relative to the lengths of these neighborhoods
- Research Organization:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE Director, Office of Science. Office of AdvancedScientific Computing Research. Mathematical, Information, andComputational Sciences Division; National Science Foundation
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 886604
- Report Number(s):
- LBNL--53656-Journal; BnR: YN0100000
- Journal Information:
- Proceedings of the American Mathematical Society, Journal Name: Proceedings of the American Mathematical Society Vol. 134
- Country of Publication:
- United States
- Language:
- English
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