Liouville numbers, Liouville sets and Liouville fields

2013/12/26 by K. Senthil Kumar, Kumar, K. Senthil, R. Thangadurai +3
Mathematics · #11J81 #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1312.7151

openalex publication_date 2013/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following earlier work by E.Maillet 100 years ago, we introduce the definition of a Liouville set, which extends the definition of a Liouville number. We also define a Liouville field, which is a field generated by a Liouville set. Any Liouville number belongs to a Liouville set S having the power of continuum and such that the union of S with the rational number field is a Liouville field.

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