On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France

DOI10.1007/BF02392563zbMath1175.11036arXivmath/0403522WikidataQ56699872 ScholiaQ56699872MaRDI QIDQ557401

Publication date: 29 June 2005

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403522

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Approximation to algebraic numbers (11J68) Schmidt Subspace Theorem and applications (11J87)

Related Items (17)

APPROXIMATION OF AN ALGEBRAIC NUMBER BY PRODUCTS OF RATIONAL NUMBERS AND UNITS ⋮ Fractional parts of powers of real algebraic numbers ⋮ On the Powers of Some Transcendental Numbers ⋮ On simultaneous approximation of algebraic numbers ⋮ Some arithmetical properties of convergents to algebraic numbers ⋮ D-finiteness, rationality, and height ⋮ A note on trace of powers of algebraic numbers ⋮ A transcendence criterion for infinite products ⋮ A note on the transcendence of infinite products ⋮ On the period of the continued fraction expansion of \(\sqrt{2^{2n+1}+1}\) ⋮ A lower estimate for \(\| e^n \|\) ⋮ On the evolution of continued fractions in a fixed quadratic field ⋮ A Mahler miscellany ⋮ On a problem of Mahler and Szekeres on approximation by roots of integers ⋮ Transcendency of some constants related to integer sequences of polynomial iterations ⋮ Transcendental series of reciprocals of Fibonacci and Lucas numbers ⋮ Algebraic approximations to linear combinations of powers: An extension of results by Mahler and Corvaja–Zannier

Cites Work

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