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Uspekhi Mat. Nauk, 1980, Volume 35, Issue 4(214), Pages 3–68 (Mi umn3565)  

This article is cited in 21 scientific papers (total in 21 papers)

Achievements and problems in Diophantine approximation theory

V. G. Sprindzhuk


Full text: PDF file (4270 kB)
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English version:
Russian Mathematical Surveys, 1980, 35:4, 1–80

Bibliographic databases:

UDC: 511
MSC: 11J61, 11J89, 11D59, 11D61, 11Cxx, 11E95
Received: 25.05.1979

Citation: V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Uspekhi Mat. Nauk, 35:4(214) (1980), 3–68; Russian Math. Surveys, 35:4 (1980), 1–80

Citation in format AMSBIB
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\by V.~G.~Sprindzhuk
\paper Achievements and problems in Diophantine approximation theory
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\yr 1980
\vol 35
\issue 4(214)
\pages 3--68
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\transl
\jour Russian Math. Surveys
\yr 1980
\vol 35
\issue 4
\pages 1--80
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. M. Dodson, “Geometric and probabilistic ideas in metric Diophantine approximation”, Russian Math. Surveys, 48:5 (1993), 73–102  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. B. Sevryuk, “Kam-stable Hamiltonians”, J Dyn Control Syst, 1:3 (1995), 351  crossref  mathscinet  zmath  elib
    3. M. B. Sevryuk, “The iteration-approximation decoupling in the reversible KAM theory”, Chaos, 5:3 (1995), 552  crossref  mathscinet  zmath  adsnasa  isi
    4. A. N. Starkov, “New progress in the theory of homogeneous flows”, Russian Math. Surveys, 52:4 (1997), 721–818  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Shih Ping Tung, “Sentences over Integral Domains and Their Computational Complexities”, Information and Computation, 149:2 (1999), 99  crossref
    6. Margulis G., “Diophantine approximation, lattices and flows on homogeneous spaces”, Panorama in Number Theory Or the View From Baker'S Garden, 2002, 280–310  isi
    7. V. V. Beresnevich, É. I. Kovalevskaya, “On Diophantine Approximations of Dependent Quantities in the $p$-adic Case”, Math. Notes, 73:1 (2003), 21–35  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Mariusz Urbański, “Diophantine approximation and self-conformal measures”, Journal of Number Theory, 110:2 (2005), 219  crossref
    9. Anish Ghosh, “Metric Diophantine approximation over a local field of positive characteristic”, Journal of Number Theory, 124:2 (2007), 454  crossref
    10. Amir Mohammadi, Alireza Salehi Golsefidy, “ S-Arithmetic Khintchine-Type Theorem”, GAFA Geom funct anal, 2009  crossref  mathscinet  isi
    11. Yuqing Zhang, “Diophantine exponents of affine subspaces: The simultaneous approximation case”, Journal of Number Theory, 129:8 (2009), 1976  crossref
    12. Dmitry Kleinbock, “An ‘almost all versus no’ dichotomy in homogeneous dynamics and Diophantine approximation”, Geom Dedicata, 2010  crossref
    13. Anish Ghosh, “Diophantine exponents and the Khintchine Groshev theorem”, Mh Math, 2010  crossref
    14. V. V. Beresnevich, S. L. Velani, “Simultaneous inhomogeneous Diophantine approximation on manifolds”, J. Math. Sci., 180:5 (2012), 531–541  mathnet  crossref  mathscinet  elib
    15. Victor Beresnevich, Evgeniy Zorin, “Explicit bounds for rational points near planar curves and metric Diophantine approximation”, Advances in Mathematics, 225:6 (2010), 3064  crossref
    16. DMITRY KLEINBOCK, GREGORY MARGULIS, JUNBO WANG, “METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS”, Int. J. Number Theory, 06:05 (2010), 1139  crossref
    17. Yuqing Zhang, “Multiplicative Diophantine exponents of hyperplanes and their nondegenerate submanifold”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2011, -  crossref
    18. A. Mohammadi, A. Salehi Golsefidy, “Simultaneous diophantine approximation in non-degenerate p-adic manifolds”, Isr. J. Math, 2011  crossref
    19. ANISH GHOSH, “A KHINTCHINE–GROSHEV THEOREM FOR AFFINE HYPERPLANES”, Int. J. Number Theory, 07:04 (2011), 1045  crossref
    20. Dzmitry Badziahin, Victor Beresnevich, Sanju Velani, “Inhomogeneous theory of dual Diophantine approximation on manifolds”, Advances in Mathematics, 232:1 (2013), 1  crossref
    21. Victor Beresnevich, “Badly approximable points on manifolds”, Invent. math, 2015  crossref
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