\(\beta\)-expansions in algebraic function fields over finite fields

DOI10.1016/j.ffa.2005.08.008zbMath1152.11037OpenAlexW1975961310MaRDI QIDQ946893

Klaus Scheicher

Publication date: 25 September 2008

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.08.008

zbMATH Keywords

Pisot and Salem numbersradix representation in function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Radix representation; digital problems (11A63) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16)

Related Items (20)

Computation of \(L_\odot(\beta)\) for some Pisot series in \(\mathbb{F}_q((x^{- 1}))\) ⋮ Dynamical directions in numeration ⋮ Purely periodic \(\beta \)-expansions with Pisot or Salem unit base in \(\mathbb F_q((X^{-1}))\) ⋮ Continued \(\beta \)-fractions with formal power series over finite fields ⋮ Rational digit systems over finite fields and Christol's theorem ⋮ Rational Laurent series with purely periodic \(\beta\)-expansions ⋮ Diophantine approximation and beta-expansions over the field of formal Laurent series ⋮ A note on non-periodic greedy expansions in Salem base ⋮ Recurrence in \(\beta \)-expansion over formal Laurent series ⋮ A proof of the Erdős-Joó-Komornik conjecture in the case of formal power series ⋮ PURELY PERIODIC BETA-EXPANSIONS OVER LAURENT SERIES ⋮ Beta-expansion and continued fraction expansion over formal Laurent series ⋮ Lengths, periods and expansions of elements written with respect to a digit system over \(\mathbb F_q [x\)] ⋮ Syntactical and automatic properties of sets of polynomials over finite fields ⋮ Metric properties and exceptional sets of \(\beta \)-expansions over formal Laurent series ⋮ Approximation orders of formal Laurent series by \(\beta\)-expansions ⋮ Automatic \(\beta\)-expansions of formal Laurent series over finite fields ⋮ Beta-expansions of -adic numbers ⋮ Number systems and tilings over Laurent series ⋮ Dynamical Diophantine approximation of beta expansions of formal Laurent series

Cites Work

• Digit systems in polynomial rings over finite fields
• \(\beta\)-expansions and symbolic dynamics
• Generalized radix representations and dynamical systems. I
• Finite beta-expansions
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Generalized radix representations and dynamical systems II
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