On approximation of \(p\)-adic numbers by \(p\)-adic algebraic numbers

DOI10.1016/j.jnt.2004.09.007zbMath1078.11050arXiv0802.1925OpenAlexW2002857725MaRDI QIDQ2565543

È. I. Kovalevskaya, Victor V. Beresnevich, Vasilii Bernik

Publication date: 27 September 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1925

zbMATH Keywords

metric Diophantine approximationKhintchine type theorems\(p\)-adic approximation

Mathematics Subject Classification ID

Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60) Continuous, (p)-adic and abstract analogues (11K41) Approximation in non-Archimedean valuations (11J61)

Related Items (23)

Unnamed Item ⋮ \(S\)-arithmetic inhomogeneous Diophantine approximation on manifolds ⋮ Unnamed Item ⋮ Unnamed Item ⋮ QUANTITATIVE ESTIMATE FOR THE MEASURE OF A SET OF REAL NUMBERS ⋮ Diophantine Inheritance for $p$-adic measures ⋮ \(S\)-arithmetic Khintchine-type theorem ⋮ Metric Diophantine approximation over a local field of positive characteristic ⋮ Simultaneous Diophantine approximation in the real and \(p\)-adic fields with nonmonotonic error function ⋮ Simultaneous p-adic Diophantine approximation ⋮ Unnamed Item ⋮ ОЦЕНКИ СВЕРХУ И СНИЗУ ДЛЯ КОЛИЧЕСТВА АЛГЕБРАИЧЕСКИХ ТОЧЕК В КОРОТКИХ ИНТЕРВАЛАХ ⋮ On Liouville sequences in the non-Archimedean case ⋮ Unnamed Item ⋮ A divergent Khintchine theorem in the real, complex, and \(p\)-adic fields ⋮ SIMULTANEOUS DIOPHANTINE APPROXIMATION IN R2 × C × Qp ⋮ Badly approximable points for diagonal approximation in solenoids ⋮ Distinction of measures of Haar cylinders in the Dirichlet theorem for the field of p-adic numbers ⋮ Simultaneous Diophantine approximation in non-degenerate \(p\)-adic manifolds ⋮ Simultaneous Diophantine approximation in the real, complex and p–adic fields. ⋮ On the divisibility of the discriminant of an integral polynomial by prime powers ⋮ An effective estimate for the measure of the set of p-adic numbers with a given order of approximation ⋮ ON A PROBLEM OF BERNIK, KLEINBOCK AND MARGULIS

Cites Work

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• On Diophantine approximations of dependent quantities in the \(p\)-adic case
• A Groshev type theorem for convergence on manifolds
• О точном порядке приближения нуля значениями целочисленных многочленов
• Inhomogeneous diophantine approximation on polynomials in $ℚ_p$
• On approximation of real numbers by real algebraic numbers

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