Abstract
In this paper we investigate a discrepancy and a L 2 discrepancy on compact groups which were introduced by E. Hlawka and W. Fleischer. First we show that this L 2 discrepancy is a generalization of the classical diaphony and can be expressed as a finite double sum. We also give estimations of quadrature errors for smooth functions. Then we prove an inequality of Erdos-Turan type for the discrepancy on compact abelian groups and study this inequality in the case of the torus and the dyadic group.
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