Submission date: 2 September 2022

Abstract:

From a talk in the New York Number Theory Seminar on April 7, 2022.

An exponential automorphism of C is a function α : C → C such that α(z_1 + z_2) = α(z_1) + α(z_2) and &\alpha;(e^z) = e^{α(z)} for all z, z_1, z_2 in C. Jan Mycielski asked if α(ln 2) = ln 2 and if α(2^{1/k}) = 2^{1/k} for k = 2, 3, 4 and for all exponential automorphisms α. These questions are answered modulo a multiple of 2 πi and a root of unity.

Mathematics Subject Classification: 12D99, 12E12, 12E30

Keywords and phrases:

Full text arXiv 2209.01027: pdf, ps.