Erdős problem 521 · problems.science

Let $(\epsilon_k)_{k\geq 0}$ be independently uniformly chosen at random from $\{-1,1\}$ . If $R_n$ counts the number of real roots of $f_n(z)=\sum_{0\leq k\leq n}\epsilon_k z^k$ then is it true that, almost surely, $\lim_{n\to \infty}\frac{R_n}{\log n}=\frac{2}{\pi}?$

Workspace

Continue locally Open source Sign in to contribute

Open this exact Problem, source revision, and authority Repository in Workbench. This handoff does not clone, switch, upload, or execute anything.

Canvas

public preview

Source#521
→
ResultNone
→
Checks0

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

AI collaborating with humans
Erdős AI contributions wiki · 30 Apr, 2026
Machine
GPT-5.5 Pro
People
Vjekoslav Kovač
Open the source record
AI collaborating with humans
Erdős AI contributions wiki · 25 Apr, 2026
Machine
GPT-5.5 Pro
People
Vjekoslav Kovač
Open the source record

Reported activity

Search problems.science