In the present paper we study the asymptotic behavior of trigonometric products of the form ∏ k = 1 N 2 sin ( π x k ) for N → ∞ , where the numbers ω = ( x k ) k = 1 N 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.
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