Budarina, Natalia; Bernik, Vasilii; O’Donnell, Hugh New estimates for the number of integer polynomials with given discriminants. (English) Zbl 07220249 Lith. Math. J. 60, No. 1, 1-8 (2020). Reviewer: Symon Serbenyuk (Kyïv) MSC: 11J83 11J68 PDF BibTeX XML Cite \textit{N. Budarina} et al., Lith. Math. J. 60, No. 1, 1--8 (2020; Zbl 07220249) Full Text: DOI
Bernik, V.; Budarina, N.; O’Donnell, H. Discriminants of polynomials in the Archimedean and non-Archimedean metrics. (English) Zbl 1399.11124 Acta Math. Hung. 154, No. 1, 265-278 (2018). Reviewer: Artūras Dubickas (Vilnius) MSC: 11J83 11J61 11R16 PDF BibTeX XML Cite \textit{V. Bernik} et al., Acta Math. Hung. 154, No. 1, 265--278 (2018; Zbl 1399.11124) Full Text: DOI
Bernik, V. I.; Budarina, N. V.; Lunevich, A. V.; O’donnel, H. Distribution of zeros of nondegenerate functions on short cuttings. (Russian. English summary) Zbl 07197283 Chebyshevskiĭ Sb. 18, No. 4(64), 107-115 (2017). MSC: 60H PDF BibTeX XML Cite \textit{V. I. Bernik} et al., Chebyshevskiĭ Sb. 18, No. 4(64), 107--115 (2017; Zbl 07197283) Full Text: DOI MNR
Bernik, Vasili; Budarina, Natalia; Götze, Friedrich Exact upper bounds for the number of the polynomials with given discriminants. (English) Zbl 1435.11097 Lith. Math. J. 57, No. 3, 283-293 (2017). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J68 PDF BibTeX XML Cite \textit{V. Bernik} et al., Lith. Math. J. 57, No. 3, 283--293 (2017; Zbl 1435.11097) Full Text: DOI
Bernik, V. I.; Budarina, N. V.; O’Donnell, H. Discriminant values of integral polynomials in the Archimedean and non-Archimedean metrics. (Russian. English summary) Zbl 1402.11104 Dokl. Nats. Akad. Nauk Belarusi 60, No. 5, 18-23 (2016). MSC: 11J61 11J83 PDF BibTeX XML Cite \textit{V. I. Bernik} et al., Dokl. Nats. Akad. Nauk Belarusi 60, No. 5, 18--23 (2016; Zbl 1402.11104) Full Text: Link
Budarina, N. V.; Bernik, V. I.; O’Donnell, H. How does the discriminant of integer polynomials depend on the distribution of roots? (Russian. English summary) Zbl 1439.11090 Chebyshevskiĭ Sb. 16, No. 1(53), 153-162 (2015). MSC: 11C08 11R04 11R29 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Chebyshevskiĭ Sb. 16, No. 1(53), 153--162 (2015; Zbl 1439.11090) Full Text: MNR
Budarina, N. V.; Dickinson, D.; Bernik, V. I. Upper bounds for the number of integer polynomials with given discriminants. (Russian. English summary) Zbl 06964089 Tr. Inst. Mat., Minsk 23, No. 2, 29-36 (2015). MSC: 11J PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Tr. Inst. Mat., Minsk 23, No. 2, 29--36 (2015; Zbl 06964089) Full Text: MNR
Budarina, N. V.; Dickinson, D.; Bernik, V. I. Distribution of discriminants of integral polynomials with prescribed laws of factorization. (Russian. English summary) Zbl 1372.11038 Dokl. Nats. Akad. Nauk Belarusi 59, No. 3, 17-20 (2015). MSC: 11C08 11J83 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dokl. Nats. Akad. Nauk Belarusi 59, No. 3, 17--20 (2015; Zbl 1372.11038) Full Text: Link
Budarina, N. V.; Bernik, V. I.; Götze, F. Effective estimations of the measure of the sets of real numbers in which integer polynomials take small value. (English) Zbl 1370.11119 Dal’nevost. Mat. Zh. 15, No. 1, 21-37 (2015). MSC: 11R04 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dal'nevost. Mat. Zh. 15, No. 1, 21--37 (2015; Zbl 1370.11119) Full Text: MNR
Budarina, N. V.; Bernik, V. I.; O’Donnell, H. On the relation between a factorization of a polynomial resultant and the frequency of its occurrence. (Russian. English summary) Zbl 1433.11090 Tr. Inst. Mat., Minsk 22, No. 2, 9-17 (2014). MSC: 11J83 11J68 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Tr. Inst. Mat., Minsk 22, No. 2, 9--17 (2014; Zbl 1433.11090) Full Text: MNR
Budarina, N. V.; Beresnevich, V. V.; Bernik, V. I. Simultaneous Diophantine approximations with the non-monotonic right-hand side. (Russian. English summary) Zbl 1372.11069 Dokl. Nats. Akad. Nauk Belarusi 58, No. 1, 26-30 (2014). MSC: 11J13 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dokl. Nats. Akad. Nauk Belarusi 58, No. 1, 26--30 (2014; Zbl 1372.11069) Full Text: Link
Bernik, V. I.; Budarina, N.; O’Donnell, H. On regular systems of real algebraic numbers of third degree in short intervals. (English. Russian original) Zbl 1304.11065 Proc. Steklov Inst. Math. 282, Suppl. 1, S54-S66 (2013); translation from Sovrem. Probl. Mat. 17, 61-75 (2013). Reviewer: Roland Quême (Brax) MSC: 11J17 11J68 PDF BibTeX XML Cite \textit{V. I. Bernik} et al., Proc. Steklov Inst. Math. 282, S54--S66 (2013; Zbl 1304.11065); translation from Sovrem. Probl. Mat. 17, 61--75 (2013) Full Text: DOI
Bernik, Vasilii; Budarina, Natalia On arithmetic properties of integral polynomials with small values on the interval. (English) Zbl 1300.11081 Šiauliai Math. Semin. 8(16), 27-36 (2013). MSC: 11J83 PDF BibTeX XML Cite \textit{V. Bernik} and \textit{N. Budarina}, Šiauliai Math. Semin. 8(16), 27--36 (2013; Zbl 1300.11081) Full Text: Link
Budarina, N. V.; Bernik, V. I.; O’Donnell, H. Real algebraic numbers of the third degree in short intervals. (Russian. English summary) Zbl 1366.11106 Dokl. Nats. Akad. Nauk Belarusi 56, No. 4, 23-26 (2012). MSC: 11R04 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dokl. Nats. Akad. Nauk Belarusi 56, No. 4, 23--26 (2012; Zbl 1366.11106)
Budarina, N. V.; Dickinson, D.; Bernik, V. I. On real and complex roots of integer polynomials in a neighborhood of their small values. (Russian. English summary) Zbl 1267.11027 Dokl. Nats. Akad. Nauk Belarusi 55, No. 5, 18-21 (2011). MSC: 11C08 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dokl. Nats. Akad. Nauk Belarusi 55, No. 5, 18--21 (2011; Zbl 1267.11027)
Budarina, Natalia; Dickinson, Detta; Bernik, Vasili Simultaneous Diophantine approximation in the real, complex and \(p\)-adic fields. (English) Zbl 1221.11159 Math. Proc. Camb. Philos. Soc. 149, No. 2, 193-216 (2010). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J13 11J61 PDF BibTeX XML Cite \textit{N. Budarina} et al., Math. Proc. Camb. Philos. Soc. 149, No. 2, 193--216 (2010; Zbl 1221.11159) Full Text: DOI
Bernik, V.; Budarina, N.; Dickinson, D. A divergent Khintchine theorem in the real, complex, and \(p\)-adic fields. (English) Zbl 1143.11337 Lith. Math. J. 48, No. 2, 158-173 (2008). MSC: 11J68 PDF BibTeX XML Cite \textit{V. Bernik} et al., Lith. Math. J. 48, No. 2, 158--173 (2008; Zbl 1143.11337) Full Text: DOI
Budarina, N. V.; Dickinson, D.; Bernik, V. I. Khintchine’s theorem and approximation of zero by the values of integer polynomials in different metrics. (English. Russian original) Zbl 1175.11040 Dokl. Math. 75, No. 2, 201-203 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 413, No. 2, 151-153 (2007). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Dokl. Math. 75, No. 2, 201--203 (2007; Zbl 1175.11040); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 413, No. 2, 151--153 (2007) Full Text: DOI