A NOTE ON THE ALGEBRAIC INDEPENDENCE OF LIOUVILLE NUMBERS
Abstract In 1985, Adams [‘The algebraic independence of certain Liouville continued fractions’, Proc. Amer. Math. Soc. 4 (1985), 512–516] proved that any finite number of Liouville series in different bases are algebraically independent. In this paper, we prove the equivalence between algebraic and linear independence when the bases are equal.
Authors
- Luiz Gustavo Dalpizol
Institutions
- Universidade do Estado de Santa Catarina (BR)
Publication Details
- Journal
- Bulletin of the Australian Mathematical Society
- Published
- 2026-06-16
- DOI
- https://doi.org/10.1017/s0004972726101403
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00