Geodesic
Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts
Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 43-52.

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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 $\alpha$.
Keywords: distribution of fractional parts, maximum and minimum values of the remainder, bounded remainder set. 
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V. V. Krasil'shchikov; A. V. Shutov. Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts. Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 43-52. http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a4/

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