Sums of Laurent series with bounded partial quotients
Abstract
In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most $4$. Later, Cusick proved that every real number is the sum of an integer and two real numbers whose partial quotients are at least $2$. In a recent paper, the authors proved that every real number is the sum of two real numbers whose partial quotients diverge. In this paper, we prove an analogue of these results for Laurent series.
Fields of Study & Subjects
Meromorphic and Entire Functions
Advanced Mathematical Identities
semigroups and automata theory
Publication details
- Journal / source
- Combinatorics and Number Theory
- Volume
- 15
- Issue
- 1
- Pages
- 9–20
- Publication date
- 24 March 2026
- Language
- EN