Lehmer's Mahler measure problem
Let M(f) denote the Mahler measure of f. There exists a constant μ>1 such that for any f(x)∈ℤ[x], M(f)>1 → M(f)≥μ.
Mathematical statement
Let M(f) denote the Mahler measure of f.
There exists a constant μ>1 such that for any f(x)∈ℤ[x], M(f)>1 → M(f)≥μ.
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
lehmer_mahler_measure_problem
theorem lehmer_mahler_measure_problem : ∃ μ : ℝ, ∀ f : ℤ[X], μ > 1 ∧ (mahlerMeasureZ f > 1 → mahlerMeasureZ f ≥ μ) := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References