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ЖУРНАЛЫ // Труды Института математики НАН Беларуси

Тр. Ин-та матем., 2016, том 24, номер 2, страницы 14–19 (Mi timb308)

Оценка сверху для количества целочисленных многочленов четвертой степени с заданной величиной дискриминантов
В. И. Берник, О. Н. Кемеш

Литература

1. Van Der Waerden B. L., Algebra, Springer-Verlag, Berlin–Heidelberg, 1971  mathscinet  zmath
2. Beresnevich V., Bernik V., Goetze F., “Integral polinomials with small discriminants and resultants”, Adv. Math., 298 (2016), 392–412  crossref  mathscinet
3. Bugeaud Y., Approximation by algebraic numbers, Cambridge Tracts in Mathematics, 160, Cambridge University Press, Cambridge, 2004, 274 pp.  mathscinet  zmath
4. Davenport H., “A note on binary cubic forms”, Mathematika, 8 (1961), 58–62  crossref  mathscinet  zmath
5. Volkmann B., “The real cubic case of Mahler's conjecture”, Mathematika, 8 (1961), 55–57  crossref  mathscinet  zmath
6. Sprindzuk V., Mahler's problem in the metric theory of numbers, Translations of Mathematical Monographs, 25, Amer. Math. Soc., Providence RI, 1969  mathscinet
7. Mahler K., “Uber das Mass der Menge aller S-Zahlen”, Math. Ann., 106 (1932), 131–139  crossref  mathscinet  zmath
8. Bernik V., Gotze F., Kukso O., “Lower bounds for the number of integral polynomials with given order of discriminants”, Acta Arith., 133 (2008), 375–390  crossref  mathscinet  zmath
9. Gotze F., Kaliada D., Korolev M., “On the number of quadratic polynomials with bounded discriminants”, Mat. Zametki (to appear), arXiv: 1308.2091 (in Russian)
10. Gotze F., Kaliada D., Kukso O., “The asymptotic number of integral cubic polynomials with bounded heights and discriminants”, Lith. Math. J., 54:2 (2014), 150–165  crossref  mathscinet  zmath
11. Bernik V., “An application of Hausdorff dimension in the theory of Diophantine approximation”, Acta Arith., 42 (1983), 219–253 (in Russian)  crossref  mathscinet  zmath; English transl.: Amer. Math. Soc. Transl., 140 (1988), 15–44  zmath
12. Beresnevich V., “On approximation of-real numbers by real algebraic numbers”, Acta Arith., 90:2 (1999), 97–112  crossref  mathscinet  zmath
13. Bernik V., “The exact order of approximating zero by integral polynomials”, Acta Arith., 53:1 (1989), 17–28 (in Russian)  crossref  mathscinet  zmath
14. Bernik V., Budarina N., Goetze F., “Exact upper bounds for the number of the polynomials with given discriminants”, Lithuanian Mathematical Journal (to appear)  mathscinet


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