Geodesic
Means over orbits of multidimensional lattices
Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 48-66

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Two transformation groups of arbitrary multidimensional lattices are constructed. We prove the coincidence of arithmetic means of $q$-th deviations of lattices for the orbits of these transformation groups. 
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     author = {N. M. Dobrovol'skii},
     title = {Means over orbits of multidimensional lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {48--66},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/}
}
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N. M. Dobrovol'skii. Means over orbits of multidimensional lattices. Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 48-66. http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a4/