3
$\begingroup$

I need some help with this question.

Let $f(z)$ an entire function, with infinite number of zeros. I want to prove that $\lim\sup_{r \to \infty} \frac{M_{f}(r)}{r^n} = \infty$

The definition of $M_{f}(r)$ is $\sup_{|z|=r}|f(z)|$, $r\in(0,R)$ when $f$ analytic in ${|z|

Assume that $f(z) \not\equiv 0$.

Thanks.

  • 0
    What about $f(z) \equiv 0$?2011-11-29
  • 0
    Basically you're right but I think that the intention was to exclude this case. I've edited the question accordingly.2011-11-29

2 Answers 2