Geodesic
$p$-adic variant of the convergence Khintchine theorem for curves over $\Bbb Z_p$
Communications in Mathematics, Tome 10 (2002) no. 1, pp. 71-78
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11J61, 11J83 
@article{COMIM_2002_10_1_a6,
     author = {Kovalevskaya, E. I.},
     title = {$p$-adic variant of the convergence {Khintchine} theorem for curves over $\Bbb Z_p$},
     journal = {Communications in Mathematics},
     pages = {71--78},
     year = {2002},
     volume = {10},
     number = {1},
     mrnumber = {1943025},
     zbl = {1069.11027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a6/}
}
TY  - JOUR
AU  - Kovalevskaya, E. I.
TI  - $p$-adic variant of the convergence Khintchine theorem for curves over $\Bbb Z_p$
JO  - Communications in Mathematics
PY  - 2002
SP  - 71
EP  - 78
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a6/
LA  - en
ID  - COMIM_2002_10_1_a6
ER  - 
%0 Journal Article
%A Kovalevskaya, E. I.
%T $p$-adic variant of the convergence Khintchine theorem for curves over $\Bbb Z_p$
%J Communications in Mathematics
%D 2002
%P 71-78
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a6/
%G en
%F COMIM_2002_10_1_a6
Kovalevskaya, E. I. $p$-adic variant of the convergence Khintchine theorem for curves over $\Bbb Z_p$. Communications in Mathematics, Tome 10 (2002) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a6/

[1] Khintchine A.: Einige Satze uber Kettenbruche mit Anwendungen auf die Theorie der Diophantischen Approximationen. Math. Ann. 92 (1924), 115-125. | DOI | MR

[2] Mahler K.: Über Transzendente p-adische Zahlen. Compozitio Mathematica. 2 (1935), 259-275. | MR | Zbl

[3] Adams W. W.: Transcendental numbers in the p-adic domain. Amer. J. Math. 88 (1966), 279-308. | DOI | MR | Zbl

[4] Mahler K.: p-adic numbers and their functions. Cambridge, 1981. | MR | Zbl

[5] Beresnevich V., Kovalevskaya E.: A full analogue of the Khintchine theorem for planar curves in $Z_p$. Preprint, Institute of Math. NAS Belarus. 2 (556) Minsk, 2000.

[6] Bernik V., Dodson M.: Metric Diophantine approximation on manifolds. Cambridge Tracts in Math. 137, Camb. Univ. Press, Cambridge, 1999. | MR | Zbl

[7] Melnichuk, Yu.: On the metric theory of the joint Diophantine approximation of p-adic numbers. Dokl. Akad. Nauk Ukrain. SSR, Ser. A.5 (1078), 394-397.

[8] Kovalevskaya E.: The convergence Khintchine theorem for polynomials and planar p-adic curves. Tatra Mt. Math. Publ. 20 (2000), 163-172. | MR | Zbl

[9] Silaeva N.: On analogue of Schmidt's theorem for curves in 3-dimensional p-adic spase. Vesti National Acad Sci. Belarus. Phys. and Math. Ser. 4 (2001), 35-41.

[10] Beresnevich V., Vasilyev D.: An analogue of the Khintchine theorem for curves in 3-dimensional complex space. Vesti National Acad Sci. Belarus. Phys. and Math. Ser. 1 (2001), 5-7.

[11] Bernik V., Kovalevskaya E.: Extremal property of some surfaces in n-dimensional Euclidean space. Mat. Zarnetki 15 N 2, 247-254. | Zbl