Proceedings of the Japan Academy, Series A, Mathematical Sciences

Uniform distribution of some special sequences

Kazuo Goto and Takeshi Kano

Full-text: Open access

Article information

Proc. Japan Acad. Ser. A Math. Sci. Volume 61, Number 3 (1985), 83-86.

First available in Project Euclid: 19 November 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11K06: General theory of distribution modulo 1 [See also 11J71]
Secondary: 11K38: Irregularities of distribution, discrepancy [See also 11Nxx]


Goto, Kazuo; Kano, Takeshi. Uniform distribution of some special sequences. Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), no. 3, 83--86. doi:10.3792/pjaa.61.83.

Export citation


  • [1] H. Cramer: Mathematical Method of Statistics. Princeton (1946).
  • [2] L. Kuipers and H. Niederreiter: Uniform Distribution of Sequences. Wiley (1974).
  • [3] K. Nagasaka: On Benford's law. Ann. Inst. Stat. Math., vol. 36, no. 2, part A, pp.337-352 (1984).
  • [4] G. Rhin: Repartition modulo 1 de f(pn) quand f est une serie entiere. Lecture Notes in Math., vol. 475, Springer, pp. 176-244 (1975).
  • [5] E. C. Titchmarsh: The Theory of the Riemann Zeta Function. Oxford (1951).
  • [6] I. M. Vinogradov: On an estimate of trigonometric sums with prime numbers. Izv. Akad. Nauk SSSR, Ser. Mat., 12, 225-248 (1948) (in Russian).
  • [7] A. Zygmund: Trigonometric Series, vol. 1, Cambridge (1959).