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On Liouville Decompositions in Local Fields

Edward B. Burger
Proceedings of the American Mathematical Society
Vol. 124, No. 11 (Nov., 1996), pp. 3305-3310
Stable URL: http://www.jstor.org/stable/2161305
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Liouville Decompositions in Local Fields
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Abstract

In 1962 Erdős proved that every real number may be decomposed into a sum of Liouville numbers. Here we consider more general functions which decompose elements from an arbitrary local field into Liouville numbers. Several examples and applications are given. As an illustration, we prove that for any real numbers α1, α2, ..., αN, not equal to 0 or 1, there exist uncountably many Liouville numbers σ such that ασ 1, ασ 2, ..., ασ N are all Liouville numbers.

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