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Three proofs of Minkowski’s second inequality in the geometry of numbers. (English) Zbl 0217.03704
Die drei Verff. liefern je einen Beweis der bekannten Minkowskischen sogenannten 2. Ungleichung in der Geometrie der Zahlen. Der erste Beweis geht von der Weylschen Vereinfachung [H. Weyl, Proc. Lond. Math. Soc., II. Ser. 47, 268–289 (1942; Zbl 0028.34902)] des ursprünglichen Beweises Minkowskis aus. Die anderen Beweise ergänzen die von H. Davenport [Q. J. Math., Oxf. Ser. 10, 119–121 (1939; Zbl 0021.29604, JFM 65.0175.01)] angegebene Beweisvariante.

11H06 Lattices and convex bodies (number-theoretic aspects)
Full Text: DOI
[1] Cassels, An Introduction to the geometry of numbers (1959)
[2] DOI: 10.1112/plms/s2-47.1.268 · Zbl 0028.34902
[3] DOI: 10.1090/S0002-9904-1961-10614-9 · Zbl 0099.03604
[4] Davenport, Quart. J. Math. 10 pp 119– (1939)
[5] Minkowski, Geometrie der Zahlen (1896) · Zbl 0050.04807
[6] DOI: 10.1007/BF02546664 · Zbl 0017.05701
[7] Siegel, Geometry of Numbers
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