Erdős Problem 524

[mo271]

What is the conjecture

https://www.erdosproblems.com/524

For any $t\in (0,1)$ let $t=\sum_{k=1}^\infty \epsilon_k(t)2^{-k}$ (where $\epsilon_k(t)\in \{0,1\}$). What is the correct order of magnitude (for almost all $t\in(0,1)$) for
$$M_n(t)=\max_{x\in [0,1]}\left\lvert \sum_{k\leq n}\epsilon_k(t)x^k\right\rvert?$$

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else

[kieranmcshane]

I plan to work on this. I have a formalization in PR #3758 — I'll trim it to statements only per repo guidelines and link to my fork for the full proofs.