Bulletin of the Australian Mathematical Society· 2026Q2
ALGEBRAIC INDEPENDENCE OF CERTAIN LIOUVILLE NUMBERS IN NON-ARCHIMEDEAN FIELDS
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- Q2SCImago
- 2026year
Short summary
This paper proves non-Archimedean analogues of Adams' theorem, establishing the algebraic independence of Liouville-type series in p-adic numbers and function fields.
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Key points
- Proves non-Archimedean analogues of Adams' theorem on algebraic independence.
- Establishes algebraic independence for Liouville-type series in p-adic number fields.
- Establishes algebraic independence for Liouville-type series in function fields.
- Extends classical transcendence theory to non-Archimedean settings.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract The theory of Liouville numbers has played a fundamental role in transcendence theory since Liouville’s pioneering construction of explicit transcendental numbers. A classical result of Adams [‘On the algebraic independence of certain Liouville numbers’, J. Pure Appl. Algebra 13 (1) (1978), 41–47] established the algebraic independence of certain Liouville series associated with multiplicatively independent integer bases. We prove non-Archimedean analogues of Adam’s theorem in two distinct settings: the field of p -adic numbers and function fields. We establish algebraic independence results for families of Liouville-type series defined in these settings, extending Adams’ theorem from the classical real case to the non-Archimedean framework.
The authors' abstract, as published at the source. Bulletin of the Australian Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics