论文标题
指数式的自动形态和Mycielski的问题
Exponential automorphisms and a problem of Mycielski
论文作者
论文摘要
$ \ mathbf {c} $的指数自动形态是一个函数$α：\ mathbf {c} \ rightarrow \ Mathbf {c} $，使得$α（z_1 + z_2）=α（z_1）=α（z_1） +α（z_2）$和$α\ z z^z^z^z^e^z^e^e^e^e^e^e^e^e^^e^^e^c^et（ $ z，z_1，z_2 \ in \ mathbf {c} $。 Jan Mycielski询问$α（\ ln 2）= \ ln 2 $以及$ k = 2、3、4 $以及所有指数型自动形态$α$ a $α（2^{1/k}）= 2^{1/k} $。这些问题回答了Modulo $2πi$的倍数和一个团结的根源。
An exponential automorphism of $\mathbf{C}$ is a function $α: \mathbf{C} \rightarrow \mathbf{C}$ such that $α(z_1 + z_2) = α(z_1) + α(z_2)$ and $α\left( e^z \right) = e^{α(z)}$ for all $z, z_1, z_2 \in \mathbf{C}$. 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 $2πi$ and a root of unity.
