Algebraic Values of Transcendental Functions at Algebraic Points

2008/08/20 by Jing-Jing Huang, Huang, Jingjing, Diego Marques +3 · 2 citations
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0808.2766

Abstract

In this paper, the authors will prove that any subset of \QQ can be the exceptional set of some transcendental entire function. Furthermore, we could generalize this theorem to a much more general version and present a unified proof.

Cited by

• Algebraic values of transcendental power series with geometric coefficient moduli
• Auxiliary functions in transcendence proofs

Related

• Some transcendental functions with an empty exceptional set
• Some results on asymptotic versions of Mahler's problems
• A Note On Transcendental Analytic Functions With Rational Coefficients Mapping ℚ Into Itself
• A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem
• On the Exceptional Sets of Transcendental Analytic Functions in Several Variables with Integer Coefficients