Some transcendental functions that yield transcendental values for every algebraic entry

Details Some transcendental functions that yield transcendental values for every algebraic entry Some transcendental functions that yield transcendental values for every algebraic entry

2010-04-10

arxiv.org/abs/1004.1668v1

Mathematics

Number Theory

16 pages, no figures. Submitted to Indagationes Math. (April/10/2010)

Scientific paper

A transcendental function usually yields a transcendental value for an algebraic entry belonging to its domain, the algebraic exceptions forming the so-called \emph{exceptional set}. For instance, the exceptional set of the function $\,\exp(z)\,$ is the unitary set $\{0\}$, which follows from the Hermite-Lindemann theorem. In this note, we give some explicit examples of transcendental entire functions having empty exceptional sets, i.e. functions that yield transcendental values for all algebraic entries, without exceptions.

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