Geodesic
Cyclic sets of numbers and lattices
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 151-158

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The sets $\{q^n,d\}$, where $d$ is not a normal number, and the sets $D^\lambda\Lambda$, where $D$ is a diagonal matrix and $\Lambda$ is a lattice in $\mathbb{R}^n$, are investigated. 
@article{ZNSL_1987_160_a13,
     author = {B. F. Skubenko},
     title = {Cyclic sets of numbers and lattices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--158},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a13/}
}
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B. F. Skubenko. Cyclic sets of numbers and lattices. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 151-158. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a13/