Abstract
By a recent method of J. Vaaler an inequality for the spherical cap discrepancy of a point sequence on thed-dimensional sphere is established.
Similar content being viewed by others
References
Beck, J., Chen, W. L.: Irregularities of Distribution. Cambridge: Univ. Press. 1987.
Cochrane, T.: Trigonometric approximation and uniform distribution modulo one. Proc. Amer. Math. Soc.103, 695–702 (1988).
Erdös, P., Turán, P.: On a problem in the theory of uniform distribution I, II. Indag. Math.10, 370–378, 406–413 (1948).
Grabner, P. J.: Harmonische Analyse, Gleichverteilung und Ziffernentwicklungen. Dissertation. Techn. Univ. Wien 1989.
Grabner, P. J., Tichy, R. F.: Remark on an inequality of Erdös-Turán-Koksma. Anz. Österr. Akad. Wiss.127, 15–22 (1990).
Hlawka, E.: Theorie der Gleichverteilung. Mannheim-Wien-Zürich: Bibliograph. Inst. 1979.
Hlawka E.: Gleichverteilung auf Produkten von Sphären. J. reine angew. Math.330, 1–43 (1982).
Koksma, J. F.: Some theorems on diophantine inequalities. Math. Centrum Amsterdam5 (1950).
Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: J. Wiley. 1974.
Magnus, W., Oberhettinger, F., Soni, R. P.: Formulas and Theorems for the Special Functions of Mathematical Physics. Berlin-Heidelberg-New York: Springer. 1966.
Müller, C.: Spherical Harmonics. Lect. Notes Math. Berlin-Heidelberg-New York: Springer. 1966.
Schmidt, W. M.: Irregularities of distribution IV. Invent. Math.7, 55–82 (1969).
Vaaler, J. D.: Some extremal functions in Fourier analysis. Bull. Amer. Math. Soc.12, 183–216 (1985).
Weyl, H.: Über die Gleichverteilung von Zahlen modulo 1. Math. Ann.77, 313–352 (1916).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grabner, P.J. Erdös-Turán type discrepancy bounds. Monatshefte für Mathematik 111, 127–135 (1991). https://doi.org/10.1007/BF01332351
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01332351