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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 2, Pages 61–86 (Mi izv7978)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00628-а
Far Eastern Branch of the Russian Academy of Sciences 12-I-П19-01


DOI: https://doi.org/10.4213/im7978

Full text: PDF file (615 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:2, 268–292

Bibliographic databases:

UDC: 511.36+511.37
MSC: Primary 11J13; Secondary 11J17
Received: 13.03.2012
Revised: 05.04.2013

Citation: A. A. Illarionov, “On the average number of best approximations of linear forms”, Izv. RAN. Ser. Mat., 78:2 (2014), 61–86; Izv. Math., 78:2 (2014), 268–292

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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