Algebraic Numbers of the form <i>α^T</i> with <i>α</i> Algebraic and <i>T</i> Transcendental

Abstract

Let α≠1 be a positive real number and let P(x) be a non-constant rational function with algebraic coefficients. In this paper, in particular, we prove that the set of algebraic numbers of the form αP(T), with T transcendental, is dense in some open interval of R.

Keywords

• Gelfond–Schneider theorem
• algebraic numbers
• transcendence
• Schanuel’s conjecture