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Higher dimensional continued fractions. (English) Zbl 1044.11596
Summary: The higher-dimensional analogue of a continued fraction is the polyhedral surface, bounding the convex hull of the semigroup of the integer points in a simplicial cone of the Euclidean space. The article describes some conjectures and theorems, extending to such higher-dimensional continued fraction the Lagrange theorem on quadratic irrationals and the Gauss-Kuzmin statistics.

MSC:
11J70 Continued fractions and generalizations
13A99 General commutative ring theory
11A55 Continued fractions
52B70 Polyhedral manifolds
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