Simultaneous approximation of zero by values of integral polynomials with respect to different valuations

Ella I. Kovalevskaya

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 5, page 479-486
  • ISSN: 0139-9918

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Kovalevskaya, Ella I.. "Simultaneous approximation of zero by values of integral polynomials with respect to different valuations." Mathematica Slovaca 54.5 (2004): 479-486. <http://eudml.org/doc/31743>.

@article{Kovalevskaya2004,
author = {Kovalevskaya, Ella I.},
journal = {Mathematica Slovaca},
keywords = {Diophantine approximation; Khintchine theorem; integral polynomials; Lebesgue measure; Haar measure},
language = {eng},
number = {5},
pages = {479-486},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Simultaneous approximation of zero by values of integral polynomials with respect to different valuations},
url = {http://eudml.org/doc/31743},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Kovalevskaya, Ella I.
TI - Simultaneous approximation of zero by values of integral polynomials with respect to different valuations
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 5
SP - 479
EP - 486
LA - eng
KW - Diophantine approximation; Khintchine theorem; integral polynomials; Lebesgue measure; Haar measure
UR - http://eudml.org/doc/31743
ER -

References

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  1. BERESNEVICH V.-BERNIK V.-KLEINBOCK D.-MARGULIES G. A., Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate manifolds, Mosc. Math. J. 2 (2002), 203-225. MR1944505
  2. BERNIK V. I.-BORBAT V. N., Simultaneous approximation of zero values of integral polynomials in p , Proc. Steklov Inst. Math. 218 (1997), 53-68 (Translated by S. Varhromeev: MAIK Nauka/Interperiodica Publishing, Moscow). (1997) MR1642345
  3. BERNIK V. I.-DODSON M. M., Metric Diophantine Approximation on Manifolds, Cambridge Tracts in Math. 137, Cambridge Univ. Press, Cambridge, 1999. (1999) MR1727177
  4. BERNIK V.-KLEINBOCK D.-MARGULIES G. A., Khintchine type theorems on manifolds: the convergence case for standard and multiplicative versions, Int. Math. Res. Not. 9 (2001), 453-486. MR1829381
  5. BUGEAUD Y., Approximation by Algebraic Numbers, Cambridge Tracts in Math. 169, Cambridge Univ. Press, Cambridge, 2004. MR2136100
  6. HARMAN G., Metric Number Theory, London Math. Soc. Monogr. (N.S.) 18, Claredon Press, Oxford, 1998. (1998) Zbl1081.11057MR1672558
  7. KALOSHA N. I., Simultaneous approximation of zero values of integral polynomials in × p , Dokl. Nats. Akad. Nauk Belarusi 47 (2003), 19-22. MR2163815
  8. KHINTCHINE A., Einige Sätze über Kettenbrüche mit Anwendungen auf die Theorie der Diophantischen Approzimationen, Math. Ann. 92 (1924), 115-125. (1924) MR1512207
  9. KLEINBOCK D.-MARGULIES G. A., Flows on homogeneous space and Diophantine approximation on manifolds, Ann. of Math. (2) 148 (1998), 339-360. (1998) MR1652916
  10. KLEINBOCK D.-TOMANOV G., Flows on S-arithmetic homogeneous space andapplication to metric Diophantine approximation, Preprint, Max Plank Institute, Bonn 2003-65 (2003). 
  11. KOVALEVSKAYA E. I., A metric theorem on the exact order of approximation of zero by values of integral polynomials in p , Dokl. Nats. Akad. Nauk Belarusi 42 (1999), 34-36. (1999) MR1741903
  12. KOVALEVSKAYA E. I., On the exact order of approximation to zero by values of integral polynomials in p , Preprint, Institute Math. National Academy Sciences Belarus, Minsk 8 (547) (1998). (1998) 
  13. SCHMIDT W. M., Diophantine Approximation, Lecture Notes in Math. 785, Springer-Verlag, New York, 1980. (1980) Zbl0421.10019MR0568710
  14. SPRINDŽUK V. G., Mahler's Problem in Metric Number Theory, Nauka i Tehnika, Minsk, 1967 [Transl. Math. Monogr. 25, Amer. Math. Soc, Providence, R.I., 1969]. (Russian) (1967) 
  15. SPRINDŽUK V. G., Metric Theory of Diophantine Approximation, Izdatel'stvo Nauka, Moskva, 1977 [John Wiley, New York-Toronto-London, 1979 (Transl. and ed. by R. A. Silverman)]. (Russian) (1977) MR0548467
  16. ŽELUDEVICH F., Simultine diophantishe Approximationen abhängiger Grössen in mehreren Metriken, Acta Arith. 46 (1986), 285-296. (1986) MR0864263

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