By a well known result of Philipp (1975), the discrepancyDN (ω) of the sequence (nkω)k≥1 mod 1 satisfies the law of the iterated logarithm under the Hadamard gap condition nk+1/nk ≥ q > 1 (k = 1, 2, . . .). Recently Berkes, Philipp and Tichy (2006) showed that this result remains valid, under Diophantine conditions on (nk), for subexpenentially growing (nk), but in general the behavior of (nkω)...
