On the complexity of algebraic numbers

DOI10.1016/j.crma.2004.04.012zbMath1119.11019OpenAlexW1998071857WikidataQ105824933 ScholiaQ105824933MaRDI QIDQ1876890

Florian Luca, Yann Bugeaud, Boris Adamczewski

Publication date: 20 August 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.04.012

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Transcendence (general theory) (11J81) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Automata sequences (11B85)

Related Items (34)

How to prove that a sequence is not automatic ⋮ On the complexity of algebraic numbers ⋮ Continued fractions with low complexity: transcendence measures and quadratic approximation ⋮ Continued fractions and transcendental numbers ⋮ On the independence of expansions of algebraic numbers in an integer base ⋮ On a recursively defined sequence involving the prime counting function ⋮ On the expansion of some exponential periods in an integer base ⋮ On a sequence related to that of Thue-Morse and its applications ⋮ Quadratic approximation to automatic continued fractions ⋮ On the complexity of algebraic numbers, and the bit-complexity of straight-line programs1 ⋮ An arithmetical property of the real numbers generated by Thue-Morse sequence along squares ⋮ Automata methods in transcendence ⋮ On patterns occurring in binary algebraic numbers ⋮ Quantitative versions of the subspace theorem and applications ⋮ ON THE TRANSCENDENCE OF CERTAIN REAL NUMBERS ⋮ ON THE BITS COUNTING FUNCTION OF REAL NUMBERS ⋮ Purely periodic and transcendental complex continued fractions ⋮ Non-zero digits in the expansion of irrational algebraic numbers in an integer base ⋮ A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers ⋮ Diophantine approximation ⋮ On the \(b\)-ary expansion of an algebraic number ⋮ Substitutions par des motifs en dimension 1 ⋮ Dynamics forβ-shifts and Diophantine approximation ⋮ Transcendence measures for continued fractions involving repetitive or symmetric patterns ⋮ Subword complexity and finite characteristic numbers ⋮ A Mahler miscellany ⋮ Subspace Lang conjecture and some remarks on a transcendental criterion ⋮ On the computational complexity of algebraic numbers: the Hartmanis–Stearns problem revisited ⋮ Irrationality measures for some automatic real numbers ⋮ An experimental investigation of the normality of irrational algebraic numbers ⋮ Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010) ⋮ Transcendence of numbers with an expansion in a subclass of complexity 2n + 1 ⋮ Diophantine approximation of Mahler numbers ⋮ A new transcendental number from the digits of N^N

Cites Work

• Diophantine approximation
• The \(\mathfrak p\)-adic Thue-Siegel-Roth-Schmidt theorem
• Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms
• Transcendence of numbers with a low complexity expansion
• On the transcendence of real numbers with a regular expansion.
• A Liouville-like approach for the transcendence of some real numbers
• On the complexity of algebraic numbers
• Norm form equations
• A generalization of Sturmian sequences: Combinatorial structure and transcendence
• On the Computational Complexity of Algorithms
• Uniform tag sequences
• Rational approximations to algebraic numbers
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