Liouville numbers, Liouville sets and Liouville fields
Number Theory
2013-12-30 v1
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.
Keywords
Cite
@article{arxiv.1312.7151,
title = {Liouville numbers, Liouville sets and Liouville fields},
author = {K. Senthil Kumar and R. Thangadurai and M. Waldschmidt},
journal= {arXiv preprint arXiv:1312.7151},
year = {2013}
}
Comments
Proceedings of the American Mathematical Society, to appear