On simultaneous uniform approximation to a $p$-adic number and its square

DOI10.1090/S0002-9939-2010-10491-4zbMath1204.11105MaRDI QIDQ3056528

Yann Bugeaud

Publication date: 12 November 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

\(p\)-adic continued fractionsapproximation to a \(p\)-adic numbersimultaneous uniform approximation

Mathematics Subject Classification ID

Simultaneous homogeneous approximation, linear forms (11J13) Approximation in non-Archimedean valuations (11J61)

Related Items (9)

On Schneider's continued fraction map on a complete non-Archimedean field ⋮ Quadratic approximation in ℚ_p ⋮ Continued fractions in the field of 𝑝-adic numbers ⋮ Classical and uniform exponents of multiplicative \(p\)-adic approximation ⋮ Schneider's \(p\)-adic continued fractions ⋮ Simultaneous approximations to \(p\)-adic numbers and algebraic dependence via multidimensional continued fractions ⋮ Recurrent properties of quasi-periodic dynamical systems with multiple frequencies of \(p\)-adic Liouville numbers ⋮ Simultaneous approximation of a \(v\)-adic number and of its square by algebraic numbers ⋮ Construction de nombres extrémaux pour le problème de l’approximation simultanée d’un nombre et de son carré

Cites Work

• Approximation to real numbers by cubic algebraic integers. II.
• Transcendence of Sturmian or morphic continued fractions
• Simultaneous approximation to a real number and its square
• Approximation d'un nombre p-adique par des nombres algebriques
• Approximation to real numbers by cubic algebraic integers I
• Approximation to real numbers by algebraic integers

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