Article ID Journal Published Year Pages File Type
4582456 Expositiones Mathematicae 2011 10 Pages PDF
Abstract

Most well-known transcendental functions usually take transcendental values at algebraic points belonging to their domains, the algebraic exceptions forming the so-called exceptional set. For instance, the exceptional set of the function ez−2 is the set {2}, as follows from the Hermite–Lindemann theorem. In this paper, we shall use interpolation formulae to prove that any subset of Q¯ is the exceptional set of uncountably many hypertranscendental entire functions with order of growth as small as we wish. Moreover these functions are algebraically independent over CC.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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