Geodesic
On the average number of best approximations of linear forms
Izvestiya. Mathematics , Tome 78 (2014) no. 2, pp. 268-292.

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We obtain asymptotic formulae for the average number of best approximations of linear forms with rational coefficients and for the expectation of the number of best approximations of linear forms with real coefficients.
Keywords: multidimensional best approximations, $f$-best approximations of linear forms, Diophantine approximations. 
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A. A. Illarionov. On the average number of best approximations of linear forms. Izvestiya. Mathematics , Tome 78 (2014) no. 2, pp. 268-292. http://geodesic.mathdoc.fr/item/IM2_2014_78_2_a2/

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