Let $f(z)$ be an entire function which is not a monomial. Let $\nu (r)$ count the number of $z$ with $|z|=r$ such that $|f(z)|={\max }_{|z|=r}|f(z)|$. (This is a finite quantity if $f$ is not a monomial.)Is it possible for$$\mathrm{limsup}\nu (r)=\infty ?$$Is it possible for$$\mathrm{liminf}\nu (r)=\infty ?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write (M(r)=\max_{|z|=r}|f(z)|) and [ \nu(r)=|\\{z:\ |z|=r,\ |f(z)|=M(r)\\}|. ] For non‑monomial entire $f$, (\nu(r)) is finite for each (r>0).

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.