Millennium ProblemsNumber theory
Riemann Hypothesis and its generalizations
The Generalized Riemann Hypothesis asserts that all the non-trivial zeros of the Dirichlet -function of a primitive Dirichlet character have real part .
Mathematical statement
The Generalized Riemann Hypothesis asserts that all the non-trivial zeros of the Dirichlet -function of a primitive Dirichlet character have real part .
Statement source: Millennium Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
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
generalized_riemann_hypothesis
theorem generalized_riemann_hypothesis (q : ℕ) [NeZero q] (χ : DirichletCharacter ℂ q) (hχ : χ.IsPrimitive) (s : ℂ) (hs : χ.LFunction s = 0) (hs_nontrivial : s ∉ Int.cast '' trivialZeros χ) : s.re = 1 / 2 := 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