This is a preview of subscription content, log in via an institution to check access.
Literature cited
L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Interscience, New York (1974).
M. B. Levin, On Jointly Absolutely Normal Numbers [in Russian], Moscow (1980). Deposited in the All-Union Institute of Scientific and Technical Information on June 25, 1980 at No. 2602-80.
A. Renyi, “Representation for real numbers and their ergodic properties,” Acta Math. Acad. Sci. Hungar.,8, 477–497 (1957).
A. O. Gel'fond, “On a general property of number systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 6, 809–814 (1959).
Z. Parry, “On the \-expansion of real numbers,” Acta Math. Acad. Sci. Hungar.,11, 401–416 (1960).
S. Ito and I. Schiokawa, “A construction of \-normal sequences,” J. Math. Soc. Japan,27, 20–23 (1975).
A. Bertrand-Mathis, “Application de la notion d'entropie au développpement d'un nombre réel dans une base de Pisot,” Ann. Inst. Fourier,35, 1–32 (1985).
N. M. Korobov, “Numbers with bounded ratios and their applications to questions of Diophantine approximations,” Izv. Akad. Nauk SSSR, Ser. Mat.,19, No. 4, 361–380 (1955).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 48, No. 6, pp. 61–71, December, 1990.
Rights and permissions
About this article
Cite this article
Levin, M.B. Jointly absolutely normal numbers. Mathematical Notes of the Academy of Sciences of the USSR 48, 1213–1220 (1990). https://doi.org/10.1007/BF01240263
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01240263