On Weyl products and uniform distribution modulo one View Full Text


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Article Info

DATE

2018-03

AUTHORS

Christoph Aistleitner, Gerhard Larcher, Friedrich Pillichshammer, Sumaia Saad Eddin, Robert F. Tichy

ABSTRACT

In the present paper we study the asymptotic behavior of trigonometric products of the form ∏k=1N2sin(πxk) for N→∞, where the numbers ω=(xk)k=1N are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points ω, thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97–118, 1969). Furthermore, we consider the special cases when the points ω are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues. More... »

PAGES

365-395

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