Points sets with low discrepancy
Peter Kritzer, Friedrich Pillichshammer (2007)
Mathematica Slovaca
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Peter Kritzer, Friedrich Pillichshammer (2007)
Mathematica Slovaca
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Eugen Futáš (1972)
Matematický časopis
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David Cantor (1977)
Acta Arithmetica
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H. Kesten (1964)
Acta Arithmetica
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Johannes Schoißengeier (1984)
Acta Arithmetica
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P. Ney, S. Wainger (1972)
Studia Mathematica
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Mordechay B. Levin (2001)
Journal de théorie des nombres de Bordeaux
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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).
Michael Drmota, Johannes Gajdosik (1998)
Journal de théorie des nombres de Bordeaux
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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.