Using exchanged toric developments, we construct tilings of toric by bounded remainder sets. To this end, two special methods for stretching the unit cubes and a general method for multiplying toric developments are used. A multidimensional analog of Hecke’s theorem on the distribution of fractional parts is proved. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 392, 2011, pp. 95–145.
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Zhuravlev, V.G. Exchanged toric developments and bounded remainder sets. J Math Sci 184, 716–745 (2012). https://doi.org/10.1007/s10958-012-0894-0
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DOI: https://doi.org/10.1007/s10958-012-0894-0