On mean values of the $L_q$-discrepancies of point distributions
HTML articles powered by AMS MathViewer
- by
M. M. Skriganov
Translated by: the author - St. Petersburg Math. J. 24 (2013), 991-1012
- DOI: https://doi.org/10.1090/S1061-0022-2013-01276-3
- Published electronically: September 23, 2013
- PDF | Request permission
Abstract:
The study of lacunarity and statistical independence of functional series is continued in the context of the theory of uniformly distributed point sets in the unit cube.References
- József Beck and William W. L. Chen, Irregularities of distribution, Cambridge Tracts in Mathematics, vol. 89, Cambridge University Press, Cambridge, 1987. MR 903025, DOI 10.1017/CBO9780511565984
- W. W. L. Chen, On irregularities of distribution. II, Quart. J. Math. Oxford Ser. (2) 34 (1983), no. 135, 257–279. MR 711520, DOI 10.1093/qmath/34.3.257
- W. W. L. Chen and M. M. Skriganov, Explicit constructions in the classical mean squares problem in irregularities of point distribution, J. Reine Angew. Math. 545 (2002), 67–95. MR 1896098, DOI 10.1515/crll.2002.037
- N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372–414. MR 32833, DOI 10.1090/S0002-9947-1949-0032833-2
- B. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Ryady i preobrazovaniya Uolsha, “Nauka”, Moscow, 1987 (Russian). Teoriya i primeneniya. [Theory and applications]. MR 925004
- J. H. van Lint, Introduction to coding theory, 3rd ed., Graduate Texts in Mathematics, vol. 86, Springer-Verlag, Berlin, 1999. MR 1664228, DOI 10.1007/978-3-642-58575-3
- Harald Niederreiter, Nets, $(t,s)$-sequences, and algebraic curves over finite fields with many rational points, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), 1998, pp. 377–386. MR 1648171
- M. Yu. Rozenblyum and M. A. Tsfasman, Codes for the $m$-metric, Problemy Peredachi Informatsii 33 (1997), no. 1, 55–63 (Russian, with Russian summary); English transl., Problems Inform. Transmission 33 (1997), no. 1, 45–52. MR 1441528
- M. M. Skriganov, Coding theory and uniform distributions, Algebra i Analiz 13 (2001), no. 2, 191–239 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 13 (2002), no. 2, 301–337. MR 1834866
- M. M. Skriganov, Harmonic analysis on totally disconnected groups and irregularities of point distributions, J. Reine Angew. Math. 600 (2006), 25–49. MR 2283797, DOI 10.1515/CRELLE.2006.085
- M. M. Skriganov, On linear codes with large weights simultaneously for the Rosenbloom-Tsfasman and Hamming metrics, J. Complexity 23 (2007), no. 4-6, 926–936. MR 2372000, DOI 10.1016/j.jco.2007.02.004
- M. M. Skriganov, The Khinchin inequality and Chen’s theorem, Algebra i Analiz 23 (2011), no. 4, 179–204 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 23 (2012), no. 4, 761–778. MR 2893524, DOI 10.1090/S1061-0022-2012-01216-1
- —, On mean discrepancies (to preparation).
- I. M. Tsobol′, Mnogomernye kvadraturnye formuly i funktsii Khaara, Izdat. “Nauka”, Moscow, 1969 (Russian). MR 0422968
Bibliographic Information
- M. M. Skriganov
- Affiliation: St. Petersburg Branch Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
- Email: maksim88138813@mail.ru
- Received by editor(s): December 20, 2011
- Published electronically: September 23, 2013
- Additional Notes: Partially supported by RFBR (project no. 08-01-00182).
- © Copyright 2013 American Mathematical Society
- Journal: St. Petersburg Math. J. 24 (2013), 991-1012
- MSC (2010): Primary 11K38
- DOI: https://doi.org/10.1090/S1061-0022-2013-01276-3
- MathSciNet review: 3097558
Dedicated: In memory of Vladimir Savel ′evich Buslaev