×

zbMATH — the first resource for mathematics

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.

MSC:
11H06 Lattices and convex bodies (number-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.