GENERALIZATION OF GELFOND’S LEMMA TO p-ADIC CYLINDERS

1. Gelfond А. О. Transcendental and algebraic numbers. 2nd ed. Moscow, URSS, 2006. 224 p. (in Russian).

2. Bernik V. Application of the Hausdorff dimension in the theory of Diophantine approximations. Acta Arithmetica, 1983, vol. 42, no. 3, pp. 219–253.

3. Baker A., Schmidt W. M. Diophantine approximation and Hausdorff dimension. Proceedings of the London Mathematical Society, 1970, vol. s3-21, no. 1, pp. 1–11. Doi: 10.1112/plms/s3-21.1.1

4. Bernik V., Götze F. A new connection between metnic theory of Diophantine approximations and distribution of algebraic numbers. Contemporary Mathematics, 2015, pp. 33–45. Doi: 10.1090/conm/631/12594

5. Bernik V., Götze F., Kukso O. On the divisibility of the discriminant of an integral polynomia by prime powers. Lithuanian Mathematical Journal, 2008, vol. 48, no. 4, pp. 380–396. Doi: 10.1007/s10986-008-9025-5

6. Bernik, V. I., Kalosha N. Zero approximation by integer polynomials in the space ××p Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2004, no. 1, pp. 121–123 (in Russian).

7. Bernik V., Budarina N., Dickinson H. Simultaneous Diophantine approximation in the real, complex and p-adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 2010, vol. 149, no. 2, pp. 193–216. Doi: 10.1017/s0305004110000162

8. Sprindzhuk V. G. Mahler‘s problem in metric number theory. Moscow, Nauka i tekhnika Publ., 1967. 184 p. (in Russian).

9. Bernik V. I. About the exact order of approximation of zero by values of integral polynomials. Acta Arithmetica, 1989, vol. 53 no. 1, pp. 17–28 (in Russian). Doi: 10.4064/aa-53-1-17-28

10. Bernik V., Dodson M. Metric Diophantine approximation on manifolds. Cambridge University Press, 1999. 172 p. Doi: 0.1017/cbo9780511565991