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

Abstract

Let $\ord$ be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in $\ord$ is the sum of pairwise distinct units, if the unit equation $u+v=2$ has a non-trivial solution $u,v\in\ord^*$. We generalize this result and give applications to signed double-base digit expansions.

References in corpus (3)

• Lower bounds on the lengths of double-base representations
• Additive unit representations in global fields - A survey
• On linear combinations of units with bounded coefficients and double-base digit expansions

Cited by in corpus (2)

• On linear combinations of units with bounded coefficients and double-base digit expansions
• Additive unit representations in global fields - A survey