Transcendence of values of the iterated exponential function at algebraic points

Abstract: We study the transcendence of the limit $h(A)$ of the sequence: $A, A^A, A^{A^A}, \dots $. In 2010, Sondow and Marques studied the case that $A$ is rational numbers or algebraic numbers satisfying some special conditions. In this talk, we extend their results and give an asymptotic formula for the number of algebraic numbers $A$ such that $h(A)$ is algebraic. This is a joint work with Hirotaka Kobayashi and Kota Saito.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October