论文信息 - On a multidimensional generalization of Lagrange's theorem on continued fractions

On a multidimensional generalization of Lagrange's theorem on continued fractions

We prove a multidimensional analogue of the classical Lagrange theorem on continued fractions using Klein polyhedra as a multidimensional generalization of continued fractions.

Evgeny Lakshtanov | E. Lakshtanov | O. German | O N German

[1] E. Korkina. LA PERIODICITE DES FRACTIONS CONTINUES MULTIDIMENSIONNELLES , 1994 .

[2] Олег Николаевич Герман,et al. Паруса и норменные минимумы решеток@@@Sails and norm minima of lattices , 2005 .

[3] O. German. Klein polyhedra and norm minima of lattices , 2005 .

[4] J. Moussafir,et al. Convex Hulls of Integral Points , 2003 .

[5] Hiroyasu Tsuchihashi. Higher-dimensional analogues of periodic continued fractions and cusp singularities , 1983 .

[6] Klein polyhedra and lattices with positive norm minima , 2005, math/0504483.

[7] B. F. Skubenko. Minima of decomposable forms of degree n in n variables for n ≥ 3 , 1992 .

[8] O. German. Sails and norm minima of lattices , 2005 .

[9] Helmut Hasse,et al. Number Theory , 2020, An Introduction to Probabilistic Number Theory.

[10] G. Lachaud,et al. Polyèdre d'Arnol'd et voile d'un cône simplicial : analogues du théorème de Lagrange , 1993 .

[11] J. Cassels,et al. On the product of three homogeneous linear forms and indefinite ternary quadratic forms , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[12] B. F. Skubenko. Minimum of a decomposable cubic form of three variables , 1991 .