Back to Problems

erdos_516.limsup_ratio_eq_one_of_hasFejerGaps

Specification

Is it true that for all entire functions `f = ∑ aₖzⁿₖ` such that `∑' 1 / nₖ < ∞`, `limsup (fun r => ratio r f) atTop = 1`?

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
theorem erdos_516.limsup_ratio_eq_one_of_hasFejerGaps : answer(sorry) ↔
    ∀ {f : ℂ → ℂ} {n : ℕ → ℕ} (hn : HasFejerGaps n) {a : ℕ → ℂ} (ha : ∀ n, a n ≠ 0)
    (hfn : ∀ z, HasSum (fun k => a k * z ^ n k) (f z)),
    limsup (fun r => ratio r f) atTop = 1
ID: ErdosProblems__516__erdos_516.limsup_ratio_eq_one_of_hasFejerGaps
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.