p -adic variant of the convergence Khintchine theorem for curves over ℤ p

Ella I. Kovalevskaya

Acta Mathematica et Informatica Universitatis Ostraviensis (2002)

  • Volume: 10, Issue: 1, page 71-78
  • ISSN: 1804-1388

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Kovalevskaya, Ella I.. "$p$-adic variant of the convergence Khintchine theorem for curves over $\mathbb {Z}_p$." Acta Mathematica et Informatica Universitatis Ostraviensis 10.1 (2002): 71-78. <http://eudml.org/doc/23866>.

@article{Kovalevskaya2002,
author = {Kovalevskaya, Ella I.},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {diophantine approximation of -adic integers; Khintchine's theorem; approximation on curves},
language = {eng},
number = {1},
pages = {71-78},
publisher = {University of Ostrava},
title = {$p$-adic variant of the convergence Khintchine theorem for curves over $\mathbb \{Z\}_p$},
url = {http://eudml.org/doc/23866},
volume = {10},
year = {2002},
}

TY - JOUR
AU - Kovalevskaya, Ella I.
TI - $p$-adic variant of the convergence Khintchine theorem for curves over $\mathbb {Z}_p$
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 2002
PB - University of Ostrava
VL - 10
IS - 1
SP - 71
EP - 78
LA - eng
KW - diophantine approximation of -adic integers; Khintchine's theorem; approximation on curves
UR - http://eudml.org/doc/23866
ER -

References

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  1. Khintchine A., 10.1007/BF01448437, Math. Ann. 92 (1924), 115-125. (1924) MR1512207DOI10.1007/BF01448437
  2. Mahler K., Über Transzendente p-adische Zahlen, Compozitio Mathematica. 2 (1935), 259-275. (1935) Zbl0012.05302MR1556919
  3. Adams W. W., 10.2307/2373193, Amer. J. Math. 88 (1966), 279-308. (1966) Zbl0144.29301MR0197399DOI10.2307/2373193
  4. Mahler K., p-adic numbers and their functions, Cambridge, 1981. (1981) Zbl0444.12013MR0644483
  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. (1999) Zbl0933.11040MR1727177
  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. Zbl0992.11043MR1845457
  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. Zbl0287.10045

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