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Displaying similar documents to “The discrepancy of random sequences {kx}”

On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin (2001)

Journal de théorie des nombres de Bordeaux

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Let q , q 1 , ⋯ , q s ≥ 2 be integers, and let α 1 , α 2 , ⋯ be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence ( α m q n , ⋯ , α m + s - 1 q n ) m , n = 1 M N coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences ( x n ) n = 1 M N 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 ( α 1 q 1 n , ⋯ , α s q s n ) n = 1 N (Korobov’s problem).