On upper bounds for the number of minimal polynomials with bounded derivative at a root
https://doi.org/10.22405/2226-8383-2019-20-2-47-54
References
1. Baker, R. 1976, “Sprindzuk’s theorem and Hausdorff dimension”, Mathematika, vol. 23, no. 2, pp. 184–197.
2. Beresnevich, V., Bernik, V. & Götze, F. 2010, “The distribution of close conjugate algebraic numbers”, Compos. Math., vol. 146, no. 5, pp. 1165–1179.
3. Beresnevich, V., Bernik, V. & Götze, F. 2016, “Integral polynomials with small discriminants and resultants”, Advances in Mathematics., vol. 298, pp. 393–412.
4. Bernik, V. 1983, “Application of the Hausdorff dimension in the theory of Diophantine approximations”, Acta Arith., vol. 42, no. 3, pp. 219–253.
5. Bernik, V., Vasiliev, D. & Kudin, A. 2014, “On the number of integral polynomials of given degree and bounded height with small value of derivative at root of polynomial”, Trudy Instituta matematiki NAN Belarusi, vol. 22, no. 2, pp. 3–8.
6. Bernik, V. & Götze, F. 2015, “Distribution of real algebraic numbers of arbitrary degree in short intervals”, Izvestiya: Mathematics, vol. 79, no. 1, pp. 18–39.
7. Bugeaud, Y. & Mignotte, M. 2010, “Polynomial root separation” Int. J. Number Theory, vol. 6, no. 3, pp. 587–602.
8. Cassels, J. W. S. 1957, “An Introduction to Diophantine Approximation (Cambridge Tracts in Mathematics and Mathematical Physics, № 45)” – Cambridge: Cambridge University Press.
9. Evertse, J.-H. 2004, “Distances between the conjugates of an algebraic number”, Publ. Math. Debrecen, vol. 65, pp. 323–340.
10. Gelfond, A. 1952, “Transcendental and Algebraic Numbers” – Moscow.
11. Schmidt, W. 1980, “Diophantine approximation (Lecture Notes in Math. no. 785)” – Berlin: Springer.
12. Sprindzhuk, V. 1967, “Mahler’s Problem in Metric Number Theory” – Minsk: Nauka i Tehnika.
13. Tishchenko, K. 2000, “On approximation of real numbers by algebraic numbers of bounded degree”, Acta Arith., vol. 94, no. 1, pp. 1–24.
Review
For citations:
Vasilyev D.V., Kudin A.S. On upper bounds for the number of minimal polynomials with bounded derivative at a root. Chebyshevskii Sbornik. 2019;20(2):47-54. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-47-54