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Transactions of the American Mathematical Society

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Metrical theorems on fractional parts of sequences


Author: Wolfgang M. Schmidt
Journal: Trans. Amer. Math. Soc. 110 (1964), 493-518
MSC: Primary 10.33; Secondary 10.30
DOI: https://doi.org/10.1090/S0002-9947-1964-0159802-4
MathSciNet review: 0159802
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  • [1] H. Behnke, Zur Theorie der diophantischen Approximationen, Abh. Math. Sem. Univ. Hamburg 3 (1924), 261-318.
  • [2] J. W. S. Cassels, Some metrical theorems in diophantine approximation. I, Proc. Cambridge Philos. Soc. 46 (1950), 209-218. MR 0036787 (12:162b)
  • [3] -, Some metrical theorems in diophantine approximation. III, Proc. Cambridge Philos. Soc. 46 (1950), 219-225. MR 0036789 (12:162d)
  • [4] J. W. S. Cassels and H. P. F. Swinnerton-Dyer, On the product of three homogeneous linear forms and indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London A 248 (1956), 73-96. MR 0070653 (17:14f)
  • [5] P. Erdös, Some results on diophantine approximation, Acta Arith. 5 (1959), 359-369. MR 0121352 (22:12091)
  • [6] P. Erdös, and J. F. Koksma, On the uniform distribution modulo 1 of sequences $ f(n,\theta )$, Indag. Math. 11 (1949), 299-302.
  • [7] P. Erdös and P. Turan, On a problem in the theory of uniform distribution, Indag. Math. 10 (1948), 370-382 and 406-413.
  • [8] A. Khintchine, Ein Satz über Kettenbrüche, mit arithmetischen Anwendungen, Math. Z. 18 (1923), 289-306. MR 1544632
  • [9] -, Einige Sätze über Kettenbrüche mit Anwendugen auf die Theorie der diophantischen Approximationen, Math. Ann. 92 (1924), 115-125. MR 1512207
  • [10] W. J. Le Veque, On the frequency of small fractional parts in certain real sequences. III, J. Reine Angew. Math. 202 (1959), 215-220. MR 0121351 (22:12090)
  • [11] T. Nagell, Introduction to number theory, Wiley, New York, 1951. MR 0043111 (13:207b)
  • [12] W. Schmidt, A metrical theorem in diophantine approximation, Canad. J. Math. 12 (1960), 619-631. MR 0118711 (22:9482)
  • [13] P. Szüsz, Über die metrische Theorie der diophantischen Approximationen, Acta Math. Acad. Sci. Hungar. 9 (1958), 177-193. MR 0095165 (20:1671)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1964-0159802-4
Article copyright: © Copyright 1964 American Mathematical Society

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