Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Irregularities of distribution. VIII
HTML articles powered by AMS MathViewer

by Wolfgang M. Schmidt
Trans. Amer. Math. Soc. 198 (1974), 1-22
DOI: https://doi.org/10.1090/S0002-9947-1974-0360504-6

Abstract:

If ${x_1},{x_2} \ldots$ is a sequence in the unit interval $0 \leqslant x \leqslant 1$ and if $S$ is a subinterval, write $C(n,S)$ for the number of elements among ${x_1}, \ldots ,{x_n}$ which lie in $S$, minus $n$ times the length of $S$. For a well distributed sequence, $C(n,S)$ as a function of $n$ will be small. It is shown that the lengths of the intervals $S$ for which $C(n,S)(n = 1,2, \ldots )$ is bounded form at most a countable set.
References
  • Harry Kesten, On a conjecture of Erdős and Szüsz related to uniform distribution $\textrm {mod}\ 1$, Acta Arith. 12 (1966/67), 193–212. MR 209253, DOI 10.4064/aa-12-2-193-212
  • A. Ostrowski, Math. Miszellen. IX. Notiz sur Theorie der Diophantischen Approximationen, Jber. Deutsch. Math.-Verein. 36 (1927), 178-180.
  • Wolfgang M. Schmidt, Irregularities of distribution. VI, Compositio Math. 24 (1972), 63–74. MR 311590
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 10K30, 10K05
  • Retrieve articles in all journals with MSC: 10K30, 10K05
Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 198 (1974), 1-22
  • MSC: Primary 10K30; Secondary 10K05
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0360504-6
  • MathSciNet review: 0360504