Inhomogeneous diophantine approximation on polynomials in ℚ p

V. Bernik; H. Dickinson; J. Yuan

Acta Arithmetica (1999)

  • Volume: 90, Issue: 1, page 37-48
  • ISSN: 0065-1036

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V. Bernik, H. Dickinson, and J. Yuan. "Inhomogeneous diophantine approximation on polynomials in $ℚ_p$." Acta Arithmetica 90.1 (1999): 37-48. <http://eudml.org/doc/207313>.

@article{V1999,
author = {V. Bernik, H. Dickinson, J. Yuan},
journal = {Acta Arithmetica},
keywords = {inhomogeneous diophantine approximation; -adic approximation; Mahler conjecture; Sprindzhuk theorem},
language = {eng},
number = {1},
pages = {37-48},
title = {Inhomogeneous diophantine approximation on polynomials in $ℚ_p$},
url = {http://eudml.org/doc/207313},
volume = {90},
year = {1999},
}

TY - JOUR
AU - V. Bernik
AU - H. Dickinson
AU - J. Yuan
TI - Inhomogeneous diophantine approximation on polynomials in $ℚ_p$
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 1
SP - 37
EP - 48
LA - eng
KW - inhomogeneous diophantine approximation; -adic approximation; Mahler conjecture; Sprindzhuk theorem
UR - http://eudml.org/doc/207313
ER -

References

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  1. [1] A. Baker, On a theorem of Sprindžuk, Proc. Roy. Soc. London Ser. A 292 (1966), 92-104. Zbl0146.06302
  2. [2] V. Bernik, Application of Hausdorff dimension in the theory of Diophantine approximation, Acta Arith. 42 (1983), 219-253 (in Russian); English transl.: Amer. Math. Soc. Transl. 140 (1988), 15-44. Zbl0482.10049
  3. [3] V. Bernik and Yu. Melnichuk, Properties of integral polynomials of p-adic variables with a small norm in the disc, Vestnik L'vov. Politekhn. Inst. 182 (1985), 63-64 (in Russian). 
  4. [4] A. O. Gel'fond, Transcendental and Algebraic Numbers, GITTL, Moscow, 1952 (in Russian); English transl.: Dover, New York, 1960. 
  5. [5] E. Lutz, Sur les approximations diophantiennes linéaires et p-adiques, Actualités Sci. Indust. 1224, Hermann, 1955. 
  6. [6] K. Mahler, Über das Mass der Menge aller s-Zahlen, Math. Ann. 106 (1932), 131-139. Zbl0003.24602
  7. [7] A. Sprindžuk, A proof of Mahler's conjecture on the measure of the set of s-numbers, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 379-436 (in Russian); English transl.: Amer. Math. Soc. Transl. (2) 51 (1966), 215-272. 
  8. [8] A. Sprindžuk, Mahler's Problem in Metric Number Theory, Transl. Math. Monographs 25, Amer. Math. Soc., Providence, 1969. 

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