Algebraic approximations to linear combinations of powers: An extension of results by Mahler and Corvaja–Zannier

DOI10.1090/tran/7316zbMath1426.11069arXiv1511.08525OpenAlexW2962907105MaRDI QIDQ3120514

Niki Myrto Mavraki, Avinash Kulkarni, Khoa D. Nguyen

Publication date: 5 March 2019

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

Full work available at URL: https://arxiv.org/abs/1511.08525

zbMATH Keywords

Diophantine approximationsubspace theoremalgebraic approximationslinear recurrence sequenceslinear combinations of powers

Mathematics Subject Classification ID

Recurrences (11B37) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Approximation to algebraic numbers (11J68) Schmidt Subspace Theorem and applications (11J87)

Related Items (9)

On the Skolem problem and some related questions for parametric families of linear recurrence sequences ⋮ A general criterion for the Pólya-Carlson dichotomy and application ⋮ On simultaneous approximation of algebraic numbers ⋮ D-finiteness, rationality, and height. II: Lower bounds over a set of positive density ⋮ Some arithmetical properties of convergents to algebraic numbers ⋮ D-finiteness, rationality, and height ⋮ A Mahler miscellany ⋮ Transcendency of some constants related to integer sequences of polynomial iterations ⋮ Transcendental series of reciprocals of Fibonacci and Lucas numbers

Cites Work

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• On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France
• Diophantine equations with power sums and universal Hilbert sets
• Finiteness of integral values for the ratio of two linear recurrences
• Norm form equations
• A quantitative version of the Absolute Subspace Theorem
• On the fractional parts of the powers of a rational number (II)
• Fractional parts of powers of rationals

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