Erdős Problem #516
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
An entire function `f` is said to be of finite order if there exist numbers c, a ≥ 0 such that for all `z`, `‖f z‖ ≤ c * rexp (‖z‖ ^ a)`.
Let `f = ∑ aₖzⁿₖ` be an entire function of finite order such that `nₖ / k → ∞`. Then `limsup (fun r => ratio r f) atTop = 1`. This is proved in [Fu63].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/516.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/516
Attempts
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