Department of Mathematical Sciences

## Sone Results on the BR"{U}CK Cojecture

In 1996, for the one CM shared value of functions, R.Br\"{u}ck proposed the following famous conjecture: Let $f(z)$ be a nonconstant entire function. Suppose that $\rho_2(f)$ is not a positive integer or infinite. If $f(z)$ and $f'(z)$ share one finite value $a$ CM, then ${f'(z)-a}=c(f(z)-a)$, where $c$ is some nonzero constant, $\rho_2(f)$ is the hyper-order of $f(z)$. In this talk, we will introduce the research status of this conjecture.