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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2161305
Page Count: 6
You can always find the topics here!Topics: Real numbers, Mathematical functions, Approximation, Perceptron convergence procedure, Differentiable functions, Numbers, Mathematical sequences, Mathematics, Transcendentals, Implicit functions
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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.
Proceedings of the American Mathematical Society © 1996 American Mathematical Society