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Niederreiter, Harald

The distribution of Farey points. (English) Zbl 0248.10013

Math. Ann. 201, 341-345 (1973).
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Cited in 2 Reviews
Cited in 14 Documents

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11J71 Distribution modulo one
11M99 Zeta and \(L\)-functions: analytic theory
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\textit{H. Niederreiter}, Math. Ann. 201, 341--345 (1973; Zbl 0248.10013)
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References:

[1] Bateman, P. T.: Sequences of mass distributions on the unit circle which tend to a uniform distribution. Amer. Math. Monthly71, 165-172 (1964). · Zbl 0128.27303
[2] Erdös, P., Kac, M., van Kampen, E. R., Wintner, A.: Ramanujan sums and almost periodic functions. Studia Math.9, 43-53 (1940). · JFM 66.0169.02
[3] Franel, J.: Les suites de Farey et le problème des nombres premiers. Göttinger Nachrichten 1924, 198-201. · JFM 50.0119.01
[4] Huxley, M. N.: The distribution of Farey points, I. Acta Arith.18, 281-287 (1971). · Zbl 0224.10036
[5] Kuipers, L., Niederreiter, H.: Uniform distribution of sequences. New York: John Wiley and Sons, in print. · Zbl 0281.10001
[6] Landau, E.: Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel. Göttinger Nachrichten 1924, 202-206. · JFM 50.0119.02
[7] LeVeque, W. J.: Topics in number theory, Vol. I. Reading, Mass.: Addison-Wesley 1956. · Zbl 0070.03804
[8] Neville, E. H.: The structure of Farey series. Proc. London Math. Soc.51 (2), 132-144 (1949). · Zbl 0034.17401
[9] Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. Math. Comp.26, 793-795 (1972). · Zbl 0258.65004
[10] Pólya, G., Szegö, G.: Aufgaben und Lehrsätze aus der Analysis I, Dritte Auflage. Berlin-Göttingen-Heidelberg: Springer 1964.
[11] Walfisz, A.: Weylsche Exponentialsummen in der neueren Zahlentheorie. Berlin: VEB Deutscher Verlag der Wissenschaften 1963. · Zbl 0146.06003
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