Source labels openChecked July 26, 2026

Elliott–Halberstam conjecture

The Elliott–Halberstam conjecture: for every $\theta < 1$ and $A > 0$ there exists a constant $C > 0$ such that $\sum_{1 \le q \le x^{\theta}} E(x; q) \le \frac{C x}{\log^A x}$ for all $x > 2$ .

Number theory AMS 11

Mathematical statement

The Elliott–Halberstam conjecture: for every $\theta < 1$ and $A > 0$ there exists a constant $C > 0$ such that $\sum_{1 \le q \le x^{\theta}} E(x; q) \le \frac{C x}{\log^A x}$ for all $x > 2$ .

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

elliott_halberstam

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem elliott_halberstam (θ : ℝ) (hθ : θ < 1) (A : ℝ) (hA : 0 < A) :    ∃ C > (0 : ℝ), ∀ x : ℕ, 2 < x →      ∑ q ∈ Finset.Icc 1 ⌊(x : ℝ) ^ θ⌋₊, E x q ≤ C * x / Real.log x ^ A := 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

Pinned Formal Conjectures sourceformalization Wikipediabackground