@article{bwmeta1.element.bwnjournal-article-aav62i3p271bwm,
author = {Yoshinobu Nakai and Iekata Shiokawa},
title = {Discrepancy estimates for a class of normal numbers},
journal = {Acta Arithmetica},
volume = {62},
year = {1992},
pages = {271-284},
zbl = {0773.11050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav62i3p271bwm}
}
Yoshinobu Nakai; Iekata Shiokawa. Discrepancy estimates for a class of normal numbers. Acta Arithmetica, Tome 62 (1992) pp. 271-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav62i3p271bwm/
[000] [1] A. S. Besicovitch, The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers, Math. Z. 39 (1935), 146-156. | Zbl 0009.20002
[001] [2] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260. | Zbl 0007.33701
[002] [3] H. Davenport and P. Erdős, Note on normal decimals, Canad. J. Math. 4 (1952), 58-63. | Zbl 0046.04902
[003] [4] L.-K. Hua, Additive Theory of Prime Numbers, Transl. Math. Monographs 13, Amer. Math. Soc., Providence, Rhode Island, 1965. | Zbl 0192.39304
[004] [5] A. A. Karatsuba, Foundations of Analytic Theory of Numbers, 2nd ed., Nauka, 1983 (in Russian).
[005] [6] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974. | Zbl 0281.10001
[006] [7] L. Mirsky, A theorem on representations of integers in the scale of r, Scripta Math. 15 (1974), 11-12. | Zbl 0034.17102
[007] [8] Y.-N. Nakai and I. Shiokawa, A class of normal numbers, Japan. J. Math. 16 (1990), 17-29.
[008] [9] Y.-N. Nakai and I. Shiokawa, A class of normal numbers II, in: Number Theory and Cryptography, J. H. Loxton (ed.), London Math. Soc. Lecture Note Ser. 154, Cambridge Univ. Press, 1990, 204-210.
[009] [10] J. Schiffer, Discrepancy of normal numbers, Acta Arith. 47 (1986), 175-186. | Zbl 0556.10036
[010] [11] J. Schoißengeier, Über die Diskrepanz von Folgen (αbⁿ), Sitzungsber. Öst. Akad. Wiss. Math.-Natur. Kl. Abt. II 187 (1978), 225-235.
[011] [12] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951. | Zbl 0042.07901
[012] [13] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge Univ. Press, London 1981.
[013] [14] I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory, Nauka, 1971 (in Russian). | Zbl 0229.10020