Metrical theorems on fractional parts of sequences
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- by Wolfgang M. Schmidt PDF
- Trans. Amer. Math. Soc. 110 (1964), 493-518 Request permission
References
-
H. Behnke, Zur Theorie der diophantischen Approximationen, Abh. Math. Sem. Univ. Hamburg 3 (1924), 261-318.
- J. W. S. Cassels, Some metrical theorems in Diophantine approximation. I, Proc. Cambridge Philos. Soc. 46 (1950), 209–218. MR 36787, DOI 10.1017/s0305004100025676
- J. W. S. Cassels, Some metrical theorems of Diophantine approximation. III, Proc. Cambridge Philos. Soc. 46 (1950), 219–225. MR 36789, DOI 10.1017/s0305004100025688
- J. W. S. Cassels and H. P. F. Swinnerton-Dyer, On the product of three homogeneous linear forms and the indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London Ser. A 248 (1955), 73–96. MR 70653, DOI 10.1098/rsta.1955.0010
- P. Erdős, Some results on diophantine approximation, Acta Arith. 5 (1959), 359–369 (1959). MR 121352, DOI 10.4064/aa-5-4-359-369 P. Erdös, and J. F. Koksma, On the uniform distribution modulo 1 of sequences $f(n,\theta )$, Indag. Math. 11 (1949), 299-302. P. Erdös and P. Turan, On a problem in the theory of uniform distribution, Indag. Math. 10 (1948), 370-382 and 406-413.
- A. Khintchine, Ein Satz über Kettenbrüche, mit arithmetischen Anwendungen, Math. Z. 18 (1923), no. 1, 289–306 (German). MR 1544632, DOI 10.1007/BF01192408
- A. Khintchine, Einige Sätze über Kettenbrüche, mit Anwendungen auf die Theorie der Diophantischen Approximationen, Math. Ann. 92 (1924), no. 1-2, 115–125 (German). MR 1512207, DOI 10.1007/BF01448437
- W. J. LeVeque, On the frequency of small fractional parts in certain real sequences. III, J. Reine Angew. Math. 202 (1959), 215–220. MR 121351, DOI 10.1515/crll.1959.202.215
- Trygve Nagell, Introduction to Number Theory, John Wiley & Sons, Inc., New York; Almqvist & Wiksell, Stockholm, 1951. MR 0043111
- Wolfgang Schmidt, A metrical theorem in diophantine approximation, Canadian J. Math. 12 (1960), 619–631. MR 118711, DOI 10.4153/CJM-1960-056-0
- P. Szüsz, Über die metrische Theorie der Diophantischen Approximation, Acta Math. Acad. Sci. Hungar. 9 (1958), 177–193 (German). MR 95165, DOI 10.1007/bf02023871
Additional Information
- © Copyright 1964 American Mathematical Society
- 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