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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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