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Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

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  • Open per source608
  • Resolved per source556
  • Other source status53
Exact formal statement available604 / 1,217
With Repository-reviewed evidence2 / 1,217
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Problems

15 Problems

SelectNumberQuestionOpen
#520Let ff be a Rademacher multiplicative function. Does there exist some constant c>0c > 0 such that, almost surely, lim sup⁡N→∞∑m≤Nf(m)Nlog⁡log⁡N=c? \limsup_{N \to \infty} \frac{\sum_{m \leq N} f(m)}{\sqrt{N \log \log N}} = c? Source says openFormalized
#521Let (ϵk)k≥0(\epsilon_k)_{k\geq 0} be independently uniformly chosen at random from {−1,1}\{-1,1\}. If RnR_n counts the number of real roots of fn(z)=∑0≤k≤nϵkzkf_n(z)=\sum_{0\leq k\leq n}\epsilon_k z^k then is it true that, almost surely, lim⁡n→∞Rnlog⁡n=2π?\lim_{n\to \infty}\frac{R_n}{\log n}=\frac{2}{\pi}?Source says openFormalized
#522Let f(z)=∑0≤k≤nϵkzkf(z)=\sum_{0\leq k\leq n} \epsilon_k z^k be a random polynomial, where ϵk∈{−1,1}\epsilon_k\in \{-1,1\} independently uniformly at random for 0≤k≤n0\leq k\leq n.Source says openFormalized
#523No statement retained — open to read what the source holdsSource says provedNo formal declaration
#524No statement retained — open to read what the source holdsSource says openNo formal declaration
#525No statement retained — open to read what the source holdsSource says provedNo formal declaration
#526No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#527No statement retained — open to read what the source holdsSource says provedNo formal declaration
#529No statement retained — open to read what the source holdsSource says openNo formal declaration
#1144No statement retained — open to read what the source holdsSource says openNo formal declaration
#1164No statement retained — open to read what the source holdsSource says provedNo formal declaration
#1165No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#1166No statement retained — open to read what the source holdsSource says provedNo formal declaration
#1167The partition relation μ→(ν)1r\mu \to (\nu)^r_1 with a single color is equivalent to ν≤μ\nu \le \mu.Source says openFormalized
#1179No statement retained — open to read what the source holdsSource says provedNo formal declaration