Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

On mean values of the $ L_q$-discrepancies of point distributions


Author: M. M. Skriganov
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 991-1012
MSC (2010): Primary 11K38
DOI: https://doi.org/10.1090/S1061-0022-2013-01276-3
Published electronically: September 23, 2013
MathSciNet review: 3097558
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. J. Beck and W. W. L. Chen, Irregularities of distribution, Cambridge Tracts in Math., vol. 89, Cambridge Univ. Press, Cambridge, 1987. MR 0903025 (88m:11061)
  • 2. W. W. L. Chen, On irregularities of distribution. II, Quart. J. Math. Oxford Ser. 2 34 (1983), 257-279. MR 0711520 (85c:11065)
  • 3. 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 (2003g:11083)
  • 4. N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372-414. MR 0032833 (11:352b)
  • 5. B. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Walsh series and transforms. Theory and applications, Nauka, Moscow, 1987; English transl., Math. and its Appl. (Soviet Ser.), vol. 64, Kluwer Acad. Publ. Group, Dordrecht, 1991. MR 0925004 (89h:42031); MR 1155844 (92m:42031)
  • 6. J. H. van Lint, Introduction to coding theory, 3 ed., Grad. Texts in Math., vol. 86, Springer-Verlag, Berlin, 1999. MR 1664228 (2000a:94001)
  • 7. H. Niederreiter, Nets, $ (t,s)$-sequences, and algebraic curves over finite fields with many rational points, Proceedings of the International Congress of Mathematicians. Vol. 3 (Berlin, 1998), Doc. Math. 1998, Extra Vol. III, 377-386. MR 1648171 (99k:11090)
  • 8. M. Yu. Rozenblyum and M. A. Tsfasman, Codes for a $ m$-metric, Probl. Peredachi Inform. 33 (1997), no. 1, 55-63; English transl., Problem Inform. Transmission 33 (1997), no. 1, 45-52. MR 1441528 (98c:94023)
  • 9. M. M. Skriganov, Coding theory and uniform distributions, Algebra i Analiz 13 (2001), no. 2, 191-239; English transl., St. Petersburg Math. J. 13 (2002), no. 2, 301-337. MR 1834866 (2002g:11111)
  • 10. -, Harmonic analysis on totally disconnected groups and irregularities of point distributions, J. Reine Angew. Math. 600 (2006), 25-49. MR 2283797 (2007k:11122)
  • 11. -, On linear codes with large weights simultaneously for the Rosenbloom-Tsfasman and Hamming metrics, J. Complexity 23 (2007), 926-936. MR 2372000 (2009b:94077)
  • 12. -, Khinchin inequality and the Chen theorem, Preprint POMI 12/2010. (Russian); Algebra i Analiz 23 (2011), no. 4, 179-204; English transl., St. Petersburg Math. J. 23 (2012), no. 4, 761-778. MR 2893524 (2012m:11100)
  • 13. -, On mean discrepancies (to preparation).
  • 14. I. M. Sobol', Multidimensional quadrature formulae and Haar functions, Nauka, Moscow, 1969. (Russian) MR 0422968 (54:10952)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 11K38

Retrieve articles in all journals with MSC (2010): 11K38


Additional Information

M. M. Skriganov
Affiliation: St. Petersburg Branch Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
Email: maksim88138813@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2013-01276-3
Keywords: Uniform distributions, lacunary series, coding theory
Received by editor(s): December 20, 2011
Published electronically: September 23, 2013
Additional Notes: Partially supported by RFBR (project no. 08-01-00182).
Dedicated: In memory of Vladimir Savel′evich Buslaev
Article copyright: © Copyright 2013 American Mathematical Society

American Mathematical Society