The discrepancy of random sequences {kx}
H. Kesten (1964)
Acta Arithmetica
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H. Kesten (1964)
Acta Arithmetica
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W. K. A. Loh (1996)
Acta Arithmetica
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Michael B. Marcus, Jay Rosen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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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).
C. Hooley (1963)
Acta Arithmetica
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I. Szalay (1988)
Studia Mathematica
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J.-L. Nicolas, A. Sárközy (2000)
Journal de théorie des nombres de Bordeaux
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Let denote the number of partitions of into parts, each of which is at least . By applying the saddle point method to the generating series, an asymptotic estimate is given for , which holds for , and .
Alzer, Horst (1993)
Portugaliae mathematica
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H. Kesten, M. V. Kozlov, F. Spitzer (1975)
Compositio Mathematica
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F. Móricz, K. Tandori (1985)
Studia Mathematica
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