Let be integers, and let be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences in -dimensional unit cube . We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Korobov’s problem).
Soient des entiers et des nombres réels. Dans cet article, on montre que la borne inférieure de la discrépance de la suite double coïncide (à un facteur logarithmique près) avec la borne inférieure de la discrépance des suites ordinaires dans un cube de dimension . Nous calculons aussi une borne inférieure de la discrépance (à un facteur logarithmique près) de la suite (problème de Korobov).
@article{JTNB_2001__13_2_483_0, author = {Mordechay B. Levin}, title = {On normal lattice configurations and simultaneously normal numbers}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {483--527}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {2}, year = {2001}, doi = {10.5802/jtnb.335}, zbl = {0999.11039}, mrnumber = {1879670}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.335/} }
TY - JOUR TI - On normal lattice configurations and simultaneously normal numbers JO - Journal de Théorie des Nombres de Bordeaux PY - 2001 DA - 2001/// SP - 483 EP - 527 VL - 13 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.335/ UR - https://zbmath.org/?q=an%3A0999.11039 UR - https://www.ams.org/mathscinet-getitem?mr=1879670 UR - https://doi.org/10.5802/jtnb.335 DO - 10.5802/jtnb.335 LA - en ID - JTNB_2001__13_2_483_0 ER -
Mordechay B. Levin. On normal lattice configurations and simultaneously normal numbers. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 483-527. doi : 10.5802/jtnb.335. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.335/
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