The distribution of Farey points. (English) Zbl 0248.10013


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11J71 Distribution modulo one
11M99 Zeta and \(L\)-functions: analytic theory
Full Text: DOI EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.