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In this article we prove that, if integer polynomial Psatisfies |P(w)|p< Hw, then for  > 2n2 and sufficiently large H the root belongs to the field of p-adic numbers.

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Об авторах

N. V. Budarina
Khabarovsk Division of Institute for Applied Mathematics

H. O’Donnell
Dublin Institute of Technology

Список литературы

1. Y. V. Nesterenko, Roots of polynomials in p-adic fields. Preprint.

2. N. Budarina, H. O’Donnell, On a problem of Nesterenko: when is the closest root of a polynomial a real number? International Journal of Number Theory, 8 (2012), no. 3, 801–811.

3. A. Baker and W.M. Schmidt, Diophantine approximation and Hausdorff dimension, Proc. Lond. Math. Soc. 21 (1970), 1–11.

4. V. I. Bernik, M. M. Dodson, Metric Diophantine approximation on manifolds, Cambridge Tracts in Math., vol. 137, Cambridge Univ. Press, 1999.

5. H. Dickinson and S. Velani, Hausdorff measure and linear forms, J. reine angew. Math., 490 (1997), 1–36.

6. V. Beresnevich, On approximation of real numbers by real algebraic numbers, Acta Arith. 90 (1999), 97–112.

7. V. Bernik, N. Budarina and D. Dickinson, A divergent Khintchine theorem in the real, complex, and p-adic fields, Lith. Math. J. 48 (2008), no. 2, 158–173.

8. Y. Bugeaud, Approximation by algebraic integers and Hausdorff dimension, J. Lond. Math. Soc., 65 (2002), pp. 547–559.

9. V. I. Bernik and D. Vasiliev, Khintchine theorem for the integer polynomials of complex variable, Tr. Inst. Mat. Nats. Akad. Navuk Belarusi, 3 (1999), 10–20.

10. V. V. Beresnevich, V. I. Bernik and E. I. Kovalevskaya, On approximation of p-adic numbers by p-adic algebraic numbers, J. Number Theory, 111 (2005), no. 1, 33–56.

11. V. Bernik, An application of Hausdorff dimension in the theory of Diophantine approximation, Acta Arith. 42 (1983), 219–253.

12. V. Bernik, On the exact order of approximation of zero by values of integral polynomials, Acta Arith. 53 (1989), 17–28.

13. V. Sprindˇzuk, Mahler’s problem in the metric theory of numbers, vol. 25, Amer. Math. Soc., Providence, RI, 1969.

14. V. I. Bernik, The metric theorem on the simultaneous approximation of zero by values of integer polynomials, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980), 24–45.

15. V. Bernik, D. Dickinson and J. Yuan, Inhomogeneous diophantine approximation on polynomials in Qp, Acta Arith., 90 (1999), no. 1, 37–48.

16. Y. Bugeaud, Approximation by algebraic numbers, Cambridge Tracts in Mathematics, Cambridge, 2004.

Для цитирования:

Budarina N.V., O’Donnell H. PROBLEM OF NESTERENKO AND METHOD OF BERNIK. Чебышевский сборник. 2016;17(4):180-184.

For citation:

Budarina N.V., O’Donnell H. PROBLEM OF NESTERENKO AND METHOD OF BERNIK. Chebyshevskii Sbornik. 2016;17(4):180-184.

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ISSN 2226-8383 (Print)