A. A. Illarionov, “On the average number of best approximations of linear forms”, Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 2,Pages <nobr>61

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On the average number of best approximations of linear forms

A. A. Illarionov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences, Khabarovsk

Abstract: 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.

UDC: 511.36+511.37

MSC: Primary 11J13; Secondary 11J17

Received: 13.03.2012
Revised: 05.04.2013

DOI: 10.4213/im7978