Un polyèdre de Klein est défini comme étant l’enveloppe convexe de tous les points non nuls d’un réseau qui se trouvent dans un orthant de l’espace
A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of
@article{JTNB_2007__19_1_175_0, author = {German, Oleg N.}, title = {Klein polyhedra and lattices with positive norm minima}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {175--190}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {1}, year = {2007}, doi = {10.5802/jtnb.580}, mrnumber = {2332060}, language = {en}, url = {https://www.numdam.org/articles/10.5802/jtnb.580/} }
TY - JOUR AU - German, Oleg N. TI - Klein polyhedra and lattices with positive norm minima JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 175 EP - 190 VL - 19 IS - 1 PB - Université Bordeaux 1 UR - https://www.numdam.org/articles/10.5802/jtnb.580/ DO - 10.5802/jtnb.580 LA - en ID - JTNB_2007__19_1_175_0 ER -
%0 Journal Article %A German, Oleg N. %T Klein polyhedra and lattices with positive norm minima %J Journal de théorie des nombres de Bordeaux %D 2007 %P 175-190 %V 19 %N 1 %I Université Bordeaux 1 %U https://www.numdam.org/articles/10.5802/jtnb.580/ %R 10.5802/jtnb.580 %G en %F JTNB_2007__19_1_175_0
German, Oleg N. Klein polyhedra and lattices with positive norm minima. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 1, pp. 175-190. doi : 10.5802/jtnb.580. https://www.numdam.org/articles/10.5802/jtnb.580/
[1] O. N. German, Klein polyhedra and norm minima of lattices. Doklady Mathematics 406:3 (2006), 38–41. | MR
[2] P. Erdös, P. Gruber, J. Hammer, Lattice Points. Pitman Monographs and Surveys in Pure and Applied Mathematics 39. Longman Scientific & Technical, Harlow (1989). | MR | Zbl
[3] F. Klein, Uber eine geometrische Auffassung der gewohnlichen Kettenbruchentwichlung. Nachr. Ges. Wiss. Gottingen 3 (1895), 357–359.
[4] O. N. German, Sails and norm minima of lattices. Mat. Sb. 196:3 (2005), 31–60; English transl., Russian Acad. Sci. Sb. Math. 196:3 (2005), 337–367. | MR | Zbl
[5] J.–O. Moussafir, Convex hulls of integral points. Zapiski nauch. sem. POMI 256 (2000). | Zbl
[6] V. I. Arnold, Continued fractions. Moscow: Moscow Center of Continuous Mathematical Education (2002).
[7] V. I. Arnold, Preface. Amer. Math. Soc. Transl. 197:2 (1999), ix–xii.
[8] E. I. Korkina, Two–dimensional continued fractions. The simplest examples. Proc. Steklov Math. Inst. RAS 209 (1995), 143–166. | MR | Zbl
[9] T. Bonnesen, W. Fenchel, Theorie der konvexen Körper. Berlin: Springer (1934). | MR | Zbl
[10] B. Grünbaum, Convex polytopes. London, New York, Sydney: Interscience Publ. (1967). | MR | Zbl
[11] P. McMullen, G. C. Shephard, Convex polytopes and the upper bound conjecture. Cambridge (GB): Cambridge University Press (1971). | MR | Zbl
[12] G. Ewald, Combinatorial convexity and algebraic geometry. Sringer–Verlag New York, Inc. (1996). | MR | Zbl
[13] Z. I. Borevich, I. R. Shafarevich, Number theory. NY Academic Press (1966). | MR | Zbl
[14] J. W. S. Cassels, H. P. F. Swinnerton–Dyer, On the product of three homogeneous linear forms and indefinite ternary quadratic forms. Phil. Trans. Royal Soc. London A 248 (1955), 73–96. | MR | Zbl
[15] B. F. Skubenko, Minima of a decomposable cubic form of three variables. Zapiski nauch. sem. LOMI 168 (1988). | Zbl
[16] B. F. Skubenko, Minima of decomposable forms of degree
[17] G. Lachaud, Voiles et Polyèdres de Klein. Act. Sci. Ind., Hermann (2002).
[18] L. Danzer, B. Grünbaum, V. Klee, Helly’s Theorem and its relatives. in Convexity (Proc. Symp. Pure Math. 7) 101–180, AMS, Providence, Rhode Island, 1963. | Zbl
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