Year: 2026
Type: article
Abstract: Let $$\mathbb{K}$$ K be an algebraic number field of degree $$k$$ k with a canonical number system $$(\alpha, \mathcal{N})$$ ( α , N ) . Denote $$S$$ S a finite set of places of $$ \mathbb{K}$$ K including the archimedean places and such that there is a place $$v\in M_\mathbb{K}\setminus S$$ v ∈ M K \ S with $$|\alpha|_v< 1$$ | α | v < 1 . Let $$u$$ u be an $$S$$ S -unit in $$\mathbb{Z}_{\mathbb{K}}$$ Z K . Then there exists an effectively computable constant $$c$$ c depending only on $$\mathbb{K}$$ K , $$\alpha$$ α and $$n$$ n , such that if the $$\alpha$$ α -representation of $$ u$$ u includes at most $$n$$ n non-zero digits then $$\ell(u)< c$$ ℓ ( u ) < c , where $$\ell(u)$$ ℓ (
Source: Analysis Mathematica
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: Debreceni Egyetem
OpenAlex ID: W7214065464