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Uniform distribution and diophantine inequalities. (English) Zbl 0538.10039

Uniformly distributed sequences with respect to the summation method \(H_{\infty}\) are investigated. Estimates for the discrepancy are established and the results are applied to certain diophantine inequalities. The article contains quantitative refinements of P. Schatte [Math. Nachr. 113, 237-243 (1983; Zbl 0526.10043)].

MSC:

11K06 General theory of distribution modulo \(1\)
11D75 Diophantine inequalities

Citations:

Zbl 0526.10043
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References:

[1] Hlawka, E.: Theorie der Gleichverteilung. Mannheim-Wien-Z?rich: B. I. 1979.
[2] Hlawka, E.: Gleichverteilung und das Konvergenzverhalten von Potenzreihen am Rande des Konvergenzkreises. Manuscr. Math.44, 231-263 (1983). · Zbl 0516.10030
[3] Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: John Wiley and Sons. 1974. · Zbl 0281.10001
[4] Niederreiter, H., Tichy, R. F.: Beitr?ge zur Diskrepanz bez?glich gewichteter Mittel. Manuscr. Math.42, 85-99 (1983). · Zbl 0498.10030
[5] Schatte, P.: Ein Kriterium f?r dieH ?-Limitierbarkeit. Math. Nachr.64, 63-70 (1974). · Zbl 0302.40010
[6] Schatte, P.: OnH ?-summability and the uniform distribution of sequences. Math. Nachr.113, 237-243 (1983). · Zbl 0526.10043
[7] Tichy, R. F.: Diskrepanz bez?glich gewichteter Mittel und Konvergenzverhalten von Potenzreihen. Manuscr. Math.44, 265-277 (1983). · Zbl 0507.10040
[8] Zeller, K., Beekmann, W.: Theorie der Limitierungsverfahren. Berlin-Heidelberg-New York: Springer. 1970. · Zbl 0199.11301
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