ON LIOUVILLE DECOMPOSITIONS IN LOCAL-FIELDS

In 1962 Erdos proved that every real number may be decomposed into a s um of Liouville numbers. Here we consider more general functions which decompose elements from an arbitrary local field into Liouville numbe rs. Several examples and applications are given. As an illustration, w e prove that for any real numbers alpha(1), alpha(2), ..., alpha(N), n ot equal to 0 or 1, there exist uncountably many Liouville numbers sig ma such that alpha(1)(sigma), alpha(2)(sigma), ..., alpha(N)(sigma) ar e all Liouville numbers.