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Weak convergence of monotone functions and Weyl's criterion

Brown, J.L. jr., Duncan, R.L. (1974)

Portugaliae mathematica

Weak Convergence of Probability nets on the Integers and the Erdos-Wintner Theorem as a Three Series Theorem

Photis Nanopoulos (1984)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Weak multipliers for generalized van der Corput sequences

Florian Pausinger (2012)

Journal de Théorie des Nombres de Bordeaux

Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base $b$ and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form $P (i) = a i (mod b)$ for coprime integers $a$ and $b$ . We show that multipliers $a$ that either divide $b - 1$ or $b + 1$ generate van der Corput sequences with weak...