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arXiv · 1312.7151

Liouville numbers, Liouville sets and Liouville fields

K. Senthil Kumar·R. Thangadurai·M. Waldschmidt
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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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K. Senthil Kumar, R. Thangadurai, M. Waldschmidt. 2013-12-26. Liouville numbers, Liouville sets and Liouville fields. https://arxiv.org/abs/1312.7151

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