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Volume 9, Issue 3

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On the Beauty of Uniform Distribution Modulo One
Karl Entacher

References

[1] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, New York: John Wiley, 1974.

[2] M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Vol. 1651 of Lecture Notes in Mathematics, Berlin: Springer, 1997.

[3] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, Philadelphia: SIAM, 1992.

[4] H. Niederreiter et al. (eds.), Monte Carlo and Quasi-Monte Carlo Methods 1996, 1998, 2000, 2002, The series of proceedings for the conferences MC&QMC 1996-2002, Springer-Verlag.

[5] P. Hellekalek and G. Larcher, Random and Quasi-Random Point Sets, Vol. 138 of Lecture Notes in Statistics, Berlin: Springer, 1998.

[6] MathConsult, "MathDirect Mathematical Software." (Jan 22, 2000) www.mathdirect.com/products.

[7] K. Entacher, "Discrepancy Estimates Based on Haar Functions," Mathematics and Computers in Simulation, 55, 2001 pp. 49-57.

[8] D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 3rd ed., Boston: Addison-Wesley, 1997.

[9] S. K. Park and K. W. Miller, "Random Number Generators: Good Ones Are Hard to Find," Communications of the Association for Computing Machinery, 31, 1988 pp. 1192-1201.

[10] B. Hechenleitner and K. Entacher, "The Spectral Test Server," (Sep 1, 2004) spectral.fh-sbg.ac.at.

[11] J. Eichenauer-Herrmann, "Statistical Independence of a New Class of Inversive Congruential Pseudorandom Numbers," Mathematics of Computation, 60, 1993 pp. 375-384.



     
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