Asymptotic properties of the spectral test, diaphony, and related quantities

This paper presents the limit laws of discrepancies defined via exponential sums, and algorithms (with error bounds) to approximate the corresponding distribution functions. The results cover the weighted and the nonweighted spectral test of Hellekalek and various instances of the general discrepancies of Hickernell and Hoogland and Kleiss for the exponential function system, as well as classical quantities like the spectral test, diaphony, and the Zaremba figure of merit.