Geodesic
A~multidimensional generalization of Heilbronn's theorem on the average length of a~finite continued fraction
Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 419-431

Voir la notice de l'article provenant de la source Math-Net.Ru

Heilbronn's theorem on the average length of a finite continued fraction is generalized to the multidimensional case in terms of relative minima of the lattices which were introduced by Voronoy and Minkowski. Bibliography: 21 titles.
Keywords: minimum of a lattice, multidimensional continued fraction, average length of a continued fraction. 
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     title = {A~multidimensional generalization of {Heilbronn's} theorem on the average length of a~finite continued fraction},
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A. A. Illarionov. A~multidimensional generalization of Heilbronn's theorem on the average length of a~finite continued fraction. Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 419-431. http://geodesic.mathdoc.fr/item/SM_2014_205_3_a4/