Description and exact maximum and minimum values of the remainder in the problem of the distribution of fractional parts
V. V. Krasil’shchikov, Антон Владимирович Шутов · Mathematical Notes · 2011
We obtain a description of the maximum and minimum values of the remainder in the problem of the distribution of fractional parts. The exact maximum and minimum values of the remainder are calculated; they are independent of the length of the bounded remainder interval. It is shown that these values can be computed in O ( m ) operations. The remainder is described as a function of the argument α .