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Erdős problem 967

Let 1<a1<⋯1<a_1<\cdots be a sequence of integers such that ∑1ai<∞\sum\frac{1}{a_i}<\infty. Is it true that, for every t∈Rt\in \mathbb{R}, 1+∑k1ak1+it≠0?1+\sum_{k}\frac{1}{a_k^{1+it}}\neq 0?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/967.lean

Formal Conjectures

FormalConjectures/ErdosProblems/967.leanErdos967.erdos_9673 linesExact file
False ↔  ∀ (a : ℕ → ℕ),    StrictMono a → 1 < a 0 → (Summable fun k => 1 / ↑(a k)) → ∀ (t : ℝ), 1 + ∑' (k : ℕ), Erdos967.summand t (a k) ≠ 0
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:967
  • PLBY Lean proofsErdosProblems.Erdos967

Reported activity

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

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