Erdős problem 967 · problems.science

Let $1<a_1<\cdots$ be a sequence of integers such that $\sum\frac{1}{a_i}<\infty$ . Is it true that, for every $t\in \mathbb{R}$ , $1+\sum_{k}\frac{1}{a_k^{1+it}}\neq 0?$

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

967.lean

Retained formal statement5 of 5

Yip [Yi25] has proved that this is not always true - in fact, for any real $t\neq 0$ , there exists a sequence of integers $1<a_1<\cdots$ such that $\sum \frac{1}{a_i}<\infty$ and $1+\sum_{k}\frac{1}{a_k^{1+it}}=0$ .

FormalConjectures/ErdosProblems/967.leanErdos967.erdos_967.variants.yip2 linesExact file

1∀ (t : ℝ),2  t ≠ 0 → ∃ a, StrictMono a ∧ 1 < a 0 ∧ (Summable fun k => 1 / ↑(a k)) ∧ 1 + ∑' (k : ℕ), Erdos967.summand t (a k) = 0

SolvedStatement only, no proof

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