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Beiträge zum Umkehrproblem für den Minkowskischen Linearformensatz. (German) Zbl 0488.10028


MSC:

11H06 Lattices and convex bodies (number-theoretic aspects)
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
Full Text: DOI

References:

[1] R. P. Bambah, A. C. Woods, On a theorem of Dyson,J. Number Theory,6 (1974), 422–433. · Zbl 0294.10019 · doi:10.1016/0022-314X(74)90040-7
[2] B. J. Birch, H. P. F. Swinnerton-Dyer, On the inhomogeneous minimum of the product ofn linear forms,Mathematika,3 (1956), 25–39. · Zbl 0074.03702 · doi:10.1112/S0025579300000863
[3] H. Davenport, Note on a result of SiegelActa Arith.,2 (1936/37), 262–265.
[4] P. Gruber, Bemerkungen zum Umkehrproblem für den Minkowskischen Linearformensatz,Ann. Univ. Sci. Budapest,13 (1970), 5–10. · Zbl 0213.05902
[5] P. Gruber, Geometry of numbers. In:Beiträge zur Geometrie, Proc. Geom. Symp. Siegen 1978, 185–225, Basel, Stuttgart: Birkhäuser, 1979.
[6] E. Hlawka, Über Gitterpunkte in Parallelepipeden,J. reine angew. Math.,187 (1950), 246–252. · Zbl 0036.30901
[7] R. B. Holmes,Geometric functional analysis and its applications, Springer (New York, Heidelberg, Berlin, 1975). · Zbl 0336.46001
[8] Chao Ko, Note on the lattice points in a parallelepiped,J. London Math. Soc.,12 (1937), 40–47. · Zbl 0015.39102 · doi:10.1112/jlms/s1-12.45.40
[9] G. C. Lekkerkerker,Geometry of numbers. Groningen: Wolters-Noordhoff Amsterdam: North-Holland, 1969.
[10] L. J. Mordell, Note on an arithmetical problem on linear forms,J. London Math. Soc.,12 (1937), 34–36. · JFM 63.0152.01 · doi:10.1112/jlms/s1-12.45.34
[11] A. Oppenheim, The continued fractions associated with chains of quadratic forms,Proc. London Math. Soc.,44 (1937), 323–335. · Zbl 0019.10502
[12] G. Ramharter, Über das Umkehrproblem zum Minkowskischen Linearformensatz,Acta Arith.,36 (1980), 27–41. · Zbl 0426.10029
[13] C. A. Rogers, On theorems of Siegel and Hlawka,Annals Math.,53 (1951), 531–540. · Zbl 0042.27601 · doi:10.2307/1969570
[14] J. Surányi, Über einen Satz von G. Szekeres in der Geometrie der Zahlen,Ann. Univ. Sci. Budapest,3/4 (1960/61), 319–326.
[15] J. Surányi, Lattice point free rectangles. In:Tagungsber. Zahlentheorie, Oberwolfach 1970, 195–202. Mannheim: B. I. 1971. · Zbl 0223.10014
[16] G. Szekeres, Note on lattice points within a parallelepiped,J. London Math. Soc.,12 (1937), 36–39. · JFM 63.0152.02 · doi:10.1112/jlms/s1-12.45.36
[17] G. Szekeres, On a problem of the lattice plane,J. London Math. Soc.,12 (1937), 88–93. · Zbl 0016.36803 · doi:10.1112/jlms/s1-12.1.88
[18] P. Szüsz, Beweis eines zahlengeometrischen Satzes von G. Szekeres,Acta Math. Acad. Sci. Hungar. 7 (1956), 75–79. · Zbl 0070.04404 · doi:10.1007/BF02022966
[19] G. Ramharter, Über ein Problem von Mordell in der Geometrie der Zahlen,Monatsh. Math.,92 (1981), 143–160. · Zbl 0459.10020 · doi:10.1007/BF01303745
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