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Continuity properties of Voronoi domains. (English) Zbl 0229.10012


MSC:

11H06 Lattices and convex bodies (number-theoretic aspects)
11P21 Lattice points in specified regions
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References:

[1] Blaschke, W.: Kreis und Kugel. Jahresber. Deutsch. Math. Ver.24, 195-207 (1915). · JFM 45.0622.02
[2] Cassels, J. W. S.: An introduction to the geometry of numbers. Berlin-Göttingen-Heidelberg: Springer. 1959. · Zbl 0086.26203
[3] Dirichlet, G. L.: Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. J. reine angew. Math.40, 209-227 (1850). · ERAM 040.1103cj · doi:10.1515/crll.1850.40.209
[4] Eggleston, H. G.: Convexity. Cambridge Tracts in Math. 47, Cambridge Univ. Press 1958. · Zbl 0086.15302
[5] Mahler, K.: On lattice points inn-dimensional star-bodies I. Existence theorems. Proc. Roy. Soc. Lond. A187, 151-187 (1946). · Zbl 0060.11710 · doi:10.1098/rspa.1946.0072
[6] Minkowski, H.: Geometrie der Zahlen. Verlag Teubner 1896. · Zbl 0050.04807
[7] Nowacki, W.: Der Begriff ?Voronoischer Bereich?. Z. Kristallogr.85, 331-332 (1933). · JFM 59.1273.02
[8] Rogers, C. A.: Packing and covering. Cambridge Tracts in Math. 54, Cambridge Univ. Press 1964. · Zbl 0176.51401
[9] Voronoi, G.: Nouvelles applications des paramètres continus à la théorie des formes quadratiques II. J. reine angew. Math.134, 198-287 (1908) und136, 67-180 (1909). · JFM 39.0274.01 · doi:10.1515/crll.1908.134.198
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