Geodesic
Estimates of the Number of Relative Minima of Lattices
Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 249-259

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We prove an estimate of the number of relative minima of an arbitrary lattice (which can be noninteger and incomplete) located in a given cube. This estimate is correct up to a constant depending on the dimension and rank.
Keywords: $s$-dimensional lattice, minimum of a lattice, rank of a lattice, continued fraction, Klein polyhedron.
Mots-clés : convergent 
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     author = {A. A. Illarionov},
     title = {Estimates of the {Number} of {Relative} {Minima} of {Lattices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {249--259},
     publisher = {mathdoc},
     volume = {89},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a7/}
}
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A. A. Illarionov. Estimates of the Number of Relative Minima of Lattices. Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 249-259. http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a7/