| Title:
|
Simultaneous approximation of zero by values of integral polynomials with respect to different valuations (English) |
| Author:
|
Kovalevskaya, Ella |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
54 |
| Issue:
|
5 |
| Year:
|
2004 |
| Pages:
|
479-486 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11J61 |
| MSC:
|
11J83 |
| idZBL:
|
Zbl 1108.11050 |
| idMR:
|
MR2114619 |
| . |
| Date available:
|
2009-09-25T14:23:18Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129162 |
| . |
| Reference:
|
[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. MR 1944505 |
| Reference:
|
[2] BERNIK V. I.-BORBAT V. N.: Simultaneous approximation of zero values of integral polynomials in ${\mathbb Q}_p$.Proc. Steklov Inst. Math. 218 (1997), 53-68 (Translated by S. Varhromeev: MAIK Nauka/Interperiodica Publishing, Moscow). MR 1642345 |
| Reference:
|
[3] BERNIK V. I.-DODSON M. M.: Metric Diophantine Approximation on Manifolds.Cambridge Tracts in Math. 137, Cambridge Univ. Press, Cambridge, 1999. MR 1727177 |
| Reference:
|
[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. MR 1829381 |
| Reference:
|
[5] BUGEAUD Y.: Approximation by Algebraic Numbers.Cambridge Tracts in Math. 169, Cambridge Univ. Press, Cambridge, 2004. MR 2136100 |
| Reference:
|
[6] HARMAN G.: Metric Number Theory.London Math. Soc. Monogr. (N.S.) 18, Claredon Press, Oxford, 1998. Zbl 1081.11057, MR 1672558 |
| Reference:
|
[7] KALOSHA N. I.: Simultaneous approximation of zero values of integral polynomials in ${\mathbb R} \times {\mathbb Q}_p$.Dokl. Nats. Akad. Nauk Belarusi 47 (2003), 19-22. MR 2163815 |
| Reference:
|
[8] KHINTCHINE A.: Einige Sätze über Kettenbrüche mit Anwendungen auf die Theorie der Diophantischen Approzimationen.Math. Ann. 92 (1924), 115-125. MR 1512207 |
| Reference:
|
[9] KLEINBOCK D.-MARGULIES G. A.: Flows on homogeneous space and Diophantine approximation on manifolds.Ann. of Math. (2) 148 (1998), 339-360. MR 1652916 |
| Reference:
|
[10] KLEINBOCK D.-TOMANOV G.: Flows on S-arithmetic homogeneous space andapplication to metric Diophantine approximation.Preprint, Max Plank Institute, Bonn 2003-65 (2003). |
| Reference:
|
[11] KOVALEVSKAYA E. I.: A metric theorem on the exact order of approximation of zero by values of integral polynomials in ${\mathbb Q}_p$.Dokl. Nats. Akad. Nauk Belarusi 42 (1999), 34-36. MR 1741903 |
| Reference:
|
[12] KOVALEVSKAYA E. I.: On the exact order of approximation to zero by values of integral polynomials in ${\mathbb Q}_p$.Preprint, Institute Math. National Academy Sciences Belarus, Minsk 8 (547) (1998). |
| Reference:
|
[13] SCHMIDT W. M.: Diophantine Approximation.Lecture Notes in Math. 785, Springer-Verlag, New York, 1980. Zbl 0421.10019, MR 0568710 |
| Reference:
|
[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) |
| Reference:
|
[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) MR 0548467 |
| Reference:
|
[16] ŽELUDEVICH F.: Simultine diophantishe Approximationen abhängiger Grössen in mehreren Metriken.Acta Arith. 46 (1986), 285-296. MR 0864263 |
| . |
