TY - JOUR
T1 - On normal lattice configurations and simultaneously normal numbers
AU - Levin, Mordechay B.
N1 - Publisher Copyright:
© Université Bordeaux 1, 2001, tous droits réservés.
PY - 2001
Y1 - 2001
N2 - Let q, q1,..., qs ≥ 2 be integers, and let α1, α2,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov’s problem).
AB - Let q, q1,..., qs ≥ 2 be integers, and let α1, α2,... be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence (Formula Presented) coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences (Formula Presented) in s-dimensional unit cube (s,M,N = 1, 2,...). We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Formula Presented) (Korobov’s problem).
UR - http://www.scopus.com/inward/record.url?scp=85009727772&partnerID=8YFLogxK
U2 - 10.5802/jtnb.335
DO - 10.5802/jtnb.335
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AN - SCOPUS:85009727772
SN - 1246-7405
VL - 13
SP - 483
EP - 527
JO - Journal de Theorie des Nombres de Bordeaux
JF - Journal de Theorie des Nombres de Bordeaux
IS - 2
ER -