Characterize the set of functions $g:\mathbb{C}\setminus\{0\}\to\mathbb{C}$ with the given property > Characterize the set of holomorphic functions $g:\mathbb{C}\setminus\\{0\\}\to\mathbb{C}$ that are bounded away from zero with $|g(z)|>|z|^{-7/3}$ for all $z\in\mathbb{C}\setminus\\{0\\}$ I understand that from the inequality, it has a pole at $0$. But other than that I really don't see a method to obtain the mentioned characterization. Appreciate your help

Let $f(z)=\frac{1}{z}$. Then consider functions $h=f \circ g$. Then $|h(z)|<|z|^{\frac{7}{3}}$ Then, $h(z)$ is similar to a quadratic polynomial. This in turn characterises $g(z)$.