LAUSR

Nonautonomous bounded remainder sets are sequences of sets that admit a uniform estimation of the remainder term in the distribution of fractional parts of a linear function. In this paper, we give a complete description of nonautonomous bounded remainder sets in the case of periodic sequences. The result is also extended to certain classes of quasiperiodic sequences of sets. Our proofs are based on obtaining explicit formulas for the remainder term by using sums of fractional parts. This method is effective, i.e., it allows us to explicitly estimate the remainder term.