Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts

V. V. Krasil'shchikov; A. V. Shutov

Geodesic

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Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts

V. V. Krasil'shchikov ; A. V. Shutov

Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 43-52

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

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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     author = {V. V. Krasil'shchikov and A. V. Shutov},
     title = {Description and {Exact} {Maximum} and {Minimum} {Values} of the {Remainder} in the {Problem} of the {Distribution} of {Fractional} {Parts}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a4/}
}

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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/