On rational approximations with denominators from thin sets, ii

In the general case a real irrational number cannot be approximated by infinitely many rationalsp/q involving error terms less than q-2 when the denominatorsq are taken from a given thin set of positive integers. The distribution of irrationals which are situated in close neighborhoods of infinitely many fractionsp/q, whereq is restricted to the elements of a thin set, depends on the asymptotic behaviour of theq’s and on their arithmetic properties.