ArticleOriginal scientific text

Title

Discrepancy estimates for a class of normal numbers

Authors 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Education, Yamanashi University, Kofu, 400 Japan
  2. Department of Mathematics, Keio University, Hiyoshi, Yokohama 223, Japan

Bibliography

  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.
  2. D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260.
  3. H. Davenport and P. Erdős, Note on normal decimals, Canad. J. Math. 4 (1952), 58-63.
  4. L.-K. Hua, Additive Theory of Prime Numbers, Transl. Math. Monographs 13, Amer. Math. Soc., Providence, Rhode Island, 1965.
  5. A. A. Karatsuba, Foundations of Analytic Theory of Numbers, 2nd ed., Nauka, 1983 (in Russian).
  6. L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974.
  7. L. Mirsky, A theorem on representations of integers in the scale of r, Scripta Math. 15 (1974), 11-12.
  8. Y.-N. Nakai and I. Shiokawa, A class of normal numbers, Japan. J. Math. 16 (1990), 17-29.
  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.
  10. J. Schiffer, Discrepancy of normal numbers, Acta Arith. 47 (1986), 175-186.
  11. J. Schoißengeier, Über die Diskrepanz von Folgen (αbⁿ), Sitzungsber. Öst. Akad. Wiss. Math.-Natur. Kl. Abt. II 187 (1978), 225-235.
  12. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951.
  13. R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge Univ. Press, London 1981.
  14. I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory, Nauka, 1971 (in Russian).
Pages:
271-284
Main language of publication
English
Received
1991-07-25
Accepted
1992-01-03
Published
1992
Exact and natural sciences