title: On linear combinations of units with bounded coefficients and double-base digit expansions.
abstract: Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.
authors: Institute of Optimisation and Discrete Mathematics (Math B), Graz University of Technology, Steyrergasse 30/II, 8010 Graz, Austria.
authors: Daniel
authors: D
authors: Krenn
authors: Chair of Mathematics and Statistics, University of Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria.
authors: Jörg
authors: J
authors: Thuswaldner
authors: Institute of Analysis and Computational Number Theory (Math A), Graz University of Technology, Steyrergasse 30/II, 8010 Graz, Austria.
authors: Volker
authors: V
authors: Ziegler
keywords: Additive unit structure; Digit expansions; Unit sum number