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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 3(393), Pages 43–126 (Mi umn9354)  

This article is cited in 15 scientific papers (total in 15 papers)

Khintchine's singular Diophantine systems and their applications

N. G. Moshchevitin

M. V. Lomonosov Moscow State University

Abstract: This paper is a survey of classical and recent methods in Diophantine approximation theory and its applications related to Khintchine's results on the existence of real numbers admitting extremely good approximations by rational numbers.
Bibliography: 145 titles.

Keywords: multidimensional Diophantine approximations, Khintchine's singular systems, continued fractions, best approximations, Diophantine inequalities, transference theorems, Kozlov problem, Peres–Schlag method.

DOI: https://doi.org/10.4213/rm9354

Full text: PDF file (1336 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:3, 433–511

Bibliographic databases:

UDC: 511.36
MSC: 11Jxx
Received: 29.03.2010

Citation: N. G. Moshchevitin, “Khintchine's singular Diophantine systems and their applications”, Uspekhi Mat. Nauk, 65:3(393) (2010), 43–126; Russian Math. Surveys, 65:3 (2010), 433–511

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/umn/v65/i3/p43

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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. N. G. Moshchevitin, “A note on badly approximable affine forms and winning sets”, Mosc. Math. J., 11:1 (2011), 129–137  mathnet  crossref  mathscinet
    2. Kan I.D., Moshchevitin N.G., Chaika J., “On Minkowski diagonal functions for two real numbers”, Diophantine analysis and related fields (DARF-2011), AIP Conf. Proc., 1385, 2011, 42–48  crossref  zmath  adsnasa  isi  scopus
    3. Nikolay Moshchevitin, “Badly approximable vectors in affine subspaces: Jarník-type result”, Chebyshevskii sb., 12:2 (2011), 77–84  mathnet  mathscinet
    4. Moshchevitin N., “Exponents for three-dimensional simultaneous Diophantine approximations”, Czechoslovak Math. J., 62:1 (2012), 127–137  crossref  mathscinet  zmath  isi  elib  scopus
    5. N. G. Moshchevitin, “On certain Littlewood-like and Schmidt-like problems in inhomogeneous Diophantine approximations”, Dalnevost. matem. zhurn., 12:2 (2012), 237–254  mathnet
    6. Moshchevitin N.G., “Proof of W. M. Schmidt's conjecture concerning successive minima of a lattice”, J. Lond. Math. Soc. (2), 86:1 (2012), 129–151  crossref  mathscinet  zmath  isi  scopus
    7. Schmidt W.M., Summerer L., “Diophantine approximation and parametric geometry of numbers”, Monatsh Math., 169:1 (2013), 51–104  crossref  mathscinet  zmath  isi  elib  scopus
    8. Gozeri G.K., “On Some Power Series with Algebraic Coefficients and Liouville Numbers”, J. Inequal. Appl., 2013, 178  crossref  mathscinet  zmath  isi
    9. Berczes A., Dujella A., Hajdu L., “Some Diophantine Properties of the Sequence of S-Units”, J. Number Theory, 138 (2014), 48–68  crossref  mathscinet  zmath  isi  scopus
    10. Moshchevitin N., “A Note on Two Linear Forms”, Acta Arith., 162:1 (2014), 43–50  crossref  mathscinet  zmath  isi  scopus
    11. Moshchevitin N., “Sur une question de N. Chevallier liée à l'approximation diophantienne simultanée”, J. Theor. Nr. Bordx., 28:3 (2016), 583–595  crossref  mathscinet  zmath  isi  scopus
    12. Bugeaud Ya., “Exponents of Diophantine Approximation”, Dynamics and Analytic Number Theory, London Mathematical Society Lecture Note Series, eds. Badziahin D., Gorodnik A., Peyerimhoff N., Cambridge Univ Press, 2016, 96–135  mathscinet  isi
    13. Das T., Fishman L., Simmons D., Urbanski M., “A Variational Principle in the Parametric Geometry of Numbers, With Applications to Metric Diophantine Approximation”, C. R. Math., 355:8 (2017), 835–846  crossref  mathscinet  zmath  isi  scopus
    14. Bengoechea P., Moshchevitin N., “Badly Approximable Points in Twisted Diophantine Approximation and Hausdorff Dimension”, Acta Arith., 177:4 (2017), 301–314  crossref  mathscinet  zmath  isi  scopus
    15. Kleinbock D., Moshchevitin N., “Simultaneous Diophantine Approximation: Sums of Squares and Homogeneous Polynomials”, Acta Arith., 190:1 (2019), 87–100  crossref  isi
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