Geodesic
The average number of relative minima of three-dimensional integer lattices of a~given determinant
Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 535-562

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We obtain an asymptotic formula for the average number of relative minima of the three-dimensional complete integer lattices of a given determinant. This generalizes Heilbronn's classical result on the average length of a finite continued fraction with a fixed denominator.
Keywords: relative minimum, multidimensional continued fraction, average length of continued fractions. 
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     author = {A. A. Illarionov},
     title = {The average number of relative minima of three-dimensional integer lattices of a~given determinant},
     journal = {Izvestiya. Mathematics },
     pages = {535--562},
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     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a4/}
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A. A. Illarionov. The average number of relative minima of three-dimensional integer lattices of a~given determinant. Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 535-562. http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a4/