Distribution Functions for Subsequences of Generalized Van Der Corput Sequences

[AH] AISTLEITNER, C.-HOFER, M.: On the limit distribution of consequtive elements of the van der Corput sequence, Unif. Distrib. Theory 8 (2013), no. 1, 89-96.Search in Google Scholar

[AN] ASMAR, N. H.-NAIR, R.: Certain averages on the a-adic numbers, Proc. Amer. Math. Soc. 114 (1992) no. 1, 21-28.Search in Google Scholar

[B] BRAUER, A.: On algebraic equations with all but one root in the interior of the unit circle, Math. Nachr. 4, (1951) 250-257.Search in Google Scholar

[CFS] CORNFELD, I. P.-FORMIN, S. V.-SINAI, YA. G.: Ergodic Theory, Springer-Verlag, Berlin, 1982. 10.1007/978-1-4615-6927-5Search in Google Scholar

[DP] DICK, J.-PILLICHSHAMMER, F.: Digital nets and Sequences, Discrepancy and Quasi-Monte Carlo Integration, Cambridge University Press, Cambridge, 2010.10.1017/CBO9780511761188Search in Google Scholar

[DT] DRMOTA, M.-TICHY, R. F.: Sequences, Discrepancies and Applications. In: Lecture Notes in Mathematics Vol. 1651, Springer-Verlag, Berlin, 1997.Search in Google Scholar

[FMS] FIALOVÁ, J.-MIŠ´IK, L.-STRAUCH, O.: An asymptotic distribution function of the three-dimensional shifted van der Corput sequence, Appl. Math. 5 (2014), 2334-2359. Published Online August 2014 in SciRes: http://www.scirp.org/journal/amhttp://dx.doi.org/10.4236/am.2014.51522710.4236/am.2014.515227Open DOISearch in Google Scholar

[FS] FIALOVÁ, J.-STRAUCH, O.: On two-dimensional sequences composed by one-dimensional uniformly distibuted sequences, Unif. Distrib. Theory 6 (2011), no. 1, 101-125.Search in Google Scholar

[GHL] GRABNE, P. J.-HELLEKALEK, P.-LIARDET, P.: The dynamical point of view of low discrepancy sequences, Unif. Distrib. Theory, 7 (2012), no. 1, 11-70.Search in Google Scholar

[HJLN] HANČL, J.-JAŠŠOVÁ, A.-LERTCHOOSAKUL, P.-NAIR, R.: On the metric theory of p-adic continued fractions, Indag. Math. (N.S.) 24 (2013), no. 1, 42-56.Search in Google Scholar

[HN] HELLEKALEK, P.-NIEDERREITER, H.: Constructions of uniformly distributed sequences using the b-adic method, Unif. Distrib. Theory 6 (2011), no. 1, 185-200.Search in Google Scholar

[HR] HEWITT, E.-ROSS, K. A.: Abstract Harmonic Analysis (2nd edition), Grundlehren der Mathematishchen Wissenschaftenenm. Vol. 115. A Series of Comprehensive Studies in Mathematics. Springer Verlag, Berlin, 1979.10.1007/978-1-4419-8638-2Search in Google Scholar

[HIT] HOFER, M.-IACÒ, M. R.-TICHY, R.: Ergodic properties of β-adic Halton sequences Ergodic Theory Dyn. Syst. 35 (2015), no. 3, 895-909.Search in Google Scholar

[JLN] JAŠŠOVÁ, A.-LERTCHOOSAKUL, P.-NAIR, R.: On variants of the Halton Sequence, Monat. Math. 180 (2016), no. 4, 743-764.Search in Google Scholar

[HKLP] HOFER, R.-KRITZER, P.-LARCHER, G.-PILLICHSHAMMER, F.: Distribution properties of generalized van der Corput-Halton sequences and their subsequences, Int. J. Number Theory 5 (2009), no. 4, 719-746.Search in Google Scholar

[KN] KUIPERS, L.-NIEDERREITER, H.: Uniform Distribution of Sequences, John Wiley & Sons, New York 1974.Search in Google Scholar

[LN] LERTCHOOSAKUL, P.-NAIR, R.: Distribution functions for subsequences of the van der Corput sequence, Indag.Math. (N.S.) 24 (2013), no. 3, 593-601.Search in Google Scholar

[O] OXTOBY, J. C.: Ergodic sets. Bull. Amer. Math. Soc. 58 (1952), 116-136.10.1090/S0002-9904-1952-09580-XOpen DOISearch in Google Scholar

[N1] NAIR, R.: On asymptotic distribution of the a-adic integers, Proc. Indian Acad. Sci. Math. Sci. 107 (1997), no. 4, 363-376.Search in Google Scholar

[Ni] NINOMIYA, S.: Construction a new class of low-discrepancy sequences by using the β-adic transformation., Math. Comput. Simulation 47 (1998), no. (2), 403-418.910.1016/S0378-4754(98)00115-3Open DOISearch in Google Scholar

[P] PARRY, W.: On β-expansions of real numbers, Acta. Math. Acad. Sci. Hungar. 11 (1960), 401-416.10.1007/BF02020954Open DOISearch in Google Scholar