On linear combinations of units with bounded coefficients and double-base digit expansions

DOI10.1007/s00605-012-0443-4zbMath1325.11119arXiv1205.4833OpenAlexW1985172152WikidataQ35209180 ScholiaQ35209180MaRDI QIDQ368536

Daniel Krenn, Volker Ziegler, Jörg M. Thuswaldner

Publication date: 23 September 2013

Published in: Monatshefte für Mathematik, Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.4833

zbMATH Keywords

unitsPisot numbers\(\beta\)-expansionsadditive unit structuredigit expansionsunit sum numbers

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Number-theoretic algorithms; complexity (11Y16) Finite fields and commutative rings (number-theoretic aspects) (11T99) Cubic and quartic extensions (11R16) Radix representation; digital problems (11A63) Algebraic numbers; rings of algebraic integers (11R04) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Other number representations (11A67)

Related Items (4)

On linear combinations of units with bounded coefficients and double-base digit expansions ⋮ On distinct unit generated fields that are totally complex ⋮ Distinct unit generated totally complex quartic fields ⋮ On the minimal Hamming weight of a multi-base representation

Uses Software

• PARI/GP
• SageMath

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On linear combinations of units with bounded coefficients and double-base digit expansions
• The additive unit structure of pure quartic complex fields
• The Magma algebra system. I: The user language
• Simplest cubic fields
• Dynamical directions in numeration
• On sums of units
• Parameterized norm form equations with arithmetic progressions
• Additive unit representations in rings over global fields -- A survey
• Lower bounds on the lengths of double-base representations
• Finite beta-expansions
• Units generating the ring of integers of complex cubic fields
• The additive unit structure of complex biquadratic fields
• The Simplest Cubic Fields
• A Test for Integers Being Sums of Distinct Units Applied to Cubic Fields
• Integers Expressible as Sums of Distinct Units
• On the unit sum number of some rings
• Sums of Distinct Divisors and Sums of Distinct Units

This page was built for publication: On linear combinations of units with bounded coefficients and double-base digit expansions