A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf
.
Multidimensional Hecke theorem on the distribution of fractional parts
2012
St. Petersburg Mathematical Journal
Hecke's theorem on the distribution of fractional parts on the unit circle is generalized to the tori where vol(T D k ) and vol(T D ) denote the volumes of the tile T D k and of the torus T D . The tiles T D k in question have the following property: for the torus T D there exists a development T D ⊂ R D such that a shift S α of the torus T D is equivalent to some exchange transformation of the corresponding tiles T D k in a partition of the development T D = T D 0 T D 1 · · · T D D . The torus
doi:10.1090/s1061-0022-2012-01232-x
fatcat:wykz4z6tqjgulpepki7mqo7hnm