Minoration de discrépance en dimension deux

• Autorzy: Henri Faure , Henri Chaix
• Języki publikacji: FR
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 76
• Numer: 2
• Strony: 149-164

Daty

wydano

1996

otrzymano

1995-04-21

Twórcy

autor

Henri Faure

• Laboratoire de Mathématiques Discrètes, U.P.R. 9016 du CNRS, 163 avenue de Luminy, case 930, F-13288 Marseille Cedex 09, France

autor

Henri Chaix

• Centre de Mathématiques et d'Informatique, Université de Provence, 39 rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France

Bibliografia

• [1] J. Beck, A two dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution, Compositio Math. 72 (1989), 269-339.
• [2] H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351.
• [3] H. Faure et H. Chaix, Minoration de discrépance en dimension 2, C. R. Acad. Sci. Paris Sér. I 319 (1994), 1-4.
• [4] G. Halász, On Roth's method in the theory of irregularities of point distribution, in: Recent Progress in Analytic Number Theory, Vol. 2, Academic Press, 1981, 79-94.
• [5] J. H. Halton, On the efficiency of certain quasi-random points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960), 84-90.
• [6] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
• [7] H. Niederreiter, Low discrepancy and low dispersion sequences, J. Number Theory 30 (1988), 51-70.
• [8] K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79.
• [9] W. M. Schmidt, Irregularities of distribution, VII, Acta Arith. 21 (1972), 45-50.
• [10] I. M. Sobol', On the distribution of points in a cube and the approximate evaluation of integrals, U.S.S.R. Comput. Math. and Math. Phys. 7 (1967), 86-112.
• [11] S. Srinivasan, On two dimensional Hammersley sequences, J. Number Theory 10 (1978), 421-429.