Sone Results on the BR"{U}CK Cojecture

报告题目Sone Results on the BR\"{U}CK Cojecture








摘要The uniqueness theory of meromorphic function mainly studies conditions under which there exists essentially only one function satisfying these conditions. It is well known that any nonconstant polynomial with leading coefficient 1 is determined by its zeros. But it is not true for the transcendental entire or meromorphic functions. Therefore, how to uniquely determine a meromorphic function is interesting and complex.

   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.







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