arXiv subjects
Publications and source records attributed to M. Waldschmidt.
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.
In this paper, using an argument of P. Erdos, K. Alniacik and E. Saias, we extend earlier results on Liouville numbers, due to P. Erdos, G.J. Rieger, W. Schwarz, K. Alniacik, E. Saias, E.B. Burger. We also produce new results of algebraic independence related with Liouville numbers and Schanuel's Conjecture, in the framework of G delta-subsets.
A sharp explicit estimate is proved for the difference $e^β-α$ when $α$ and $β$ are nonzero algebraic numbers.