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, Natalia; Dickinson, Detta Inhomogeneous Diophantine approximation on integer polynomials with non-monotonic error function. (English) Zbl 1292.11086 Acta Arith. 160, No. 3, 243-257 (2013). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11K60 PDF BibTeX XML Cite \textit{N. Budarina} and \textit{D. Dickinson}, Acta Arith. 160, No. 3, 243--257 (2013; Zbl 1292.11086) Full Text: DOI
Yuan, Jin; Budarina, Natalia; Dickinson, Detta On the number of polynomials with small discriminants in the Euclidean and \(p\)-adic metrics. (English) Zbl 1275.11109 Acta Math. Sin., Engl. Ser. 28, No. 3, 469-476 (2012). Reviewer: Victor Beresnevich (Heslington) MSC: 11J83 11J54 11J61 PDF BibTeX XML Cite \textit{J. Yuan} et al., Acta Math. Sin., Engl. Ser. 28, No. 3, 469--476 (2012; Zbl 1275.11109) Full Text: DOI
Budarina, Natalia; Dickinson, Detta Simultaneous Diophantine approximation in two metrics and the distance between conjugate algebraic numbers in \(\mathbb C\times\mathbb Q_p\). (English) Zbl 1239.11075 Indag. Math., New Ser. 23, No. 1-2, 32-41 (2012). Reviewer: Enrico Zoli (Firenze) MSC: 11J13 11J83 PDF BibTeX XML Cite \textit{N. Budarina} and \textit{D. Dickinson}, Indag. Math., New Ser. 23, No. 1--2, 32--41 (2012; Zbl 1239.11075) Full Text: DOI
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)
Bugeaud, Yann; Budarina, Natalia; Dickinson, Detta; O’Donnell, Hugh On simultaneous rational approximation to a \(p\)-adic number and its integral powers. (English) Zbl 1264.11058 Proc. Edinb. Math. Soc., II. Ser. 54, No. 3, 599-612 (2011). Reviewer: Roland Quême (Brax) MSC: 11J13 11J61 PDF BibTeX XML Cite \textit{Y. Bugeaud} et al., Proc. Edinb. Math. Soc., II. Ser. 54, No. 3, 599--612 (2011; Zbl 1264.11058) Full Text: DOI
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
Budarina, Natalia; Dickinson, Detta; Levesley, Jason Simultaneous Diophantine approximation on polynomial curves. (English) Zbl 1279.11076 Mathematika 56, No. 1, 77-85 (2010). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J13 11J54 PDF BibTeX XML Cite \textit{N. Budarina} et al., Mathematika 56, No. 1, 77--85 (2010; Zbl 1279.11076) Full Text: DOI
Budarina, Natalia; Dickinson, Detta Diophantine approximation on non-degenerate curves with non-monotonic error function. (English) Zbl 1180.11025 Bull. Lond. Math. Soc. 41, No. 1, 137-146 (2009). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 PDF BibTeX XML Cite \textit{N. Budarina} and \textit{D. Dickinson}, Bull. Lond. Math. Soc. 41, No. 1, 137--146 (2009; Zbl 1180.11025) Full Text: DOI
Budarina, Natalia; Dickinson, Detta Simultaneous Diophantine approximation of integral polynomials in the different metrics. (English) Zbl 1355.11077 Chebyshevskiĭ Sb. 9, No. 1(25), 169-184 (2008). MSC: 11J83 11K60 11J54 11J61 PDF BibTeX XML Cite \textit{N. Budarina} and \textit{D. Dickinson}, Chebyshevskiĭ Sb. 9, No. 1(25), 169--184 (2008; Zbl 1355.11077) Full Text: MNR
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
Budarina, N.; Dickinson, D. Simultaneous Diophantine approximation on surfaces defined by polynomial expressions \(x^d_1+\dots+x^d_m\). (English) Zbl 1157.11032 Laurinčikas, A. (ed.) et al., Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25–29, 2006. Vilnius: TEV (ISBN 978-9955-680-81-9/hbk). 17-23 (2007). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J13 PDF BibTeX XML Cite \textit{N. Budarina} and \textit{D. Dickinson}, in: Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25--29, 2006. Vilnius: TEV. 17--23 (2007; Zbl 1157.11032)