recognition /
NumberTheory /
NumberTheory.EulerInstantiation /
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formal statement (Lean)
668 theorem eulerQuantitativeFactorization_center (ρ : ℂ)
669 (hρ_ne : ρ ≠ 1) (m : ℤ)
670 (hord : meromorphicOrderAt zetaReciprocal ρ = ↑m)
671 (hσ : 1/2 < ρ.re) :
672 (eulerQuantitativeFactorization ρ hρ_ne m hord hσ).center = ρ := by
proof body
Term-mode proof.
673 simpa [eulerQuantitativeFactorization, LocalMeromorphicWitness.shrinkRadius] using
674 (zetaReciprocal_local_factorization ρ hρ_ne m hord).choose_spec.1
675
676 /-- The order of the Euler quantitative factorization is the specified
677 meromorphic order `m`. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (13)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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eulerQuantitativeFactorization
in IndisputableMonolith.NumberTheory.EulerInstantiation
decl_use
zetaReciprocal
in IndisputableMonolith.NumberTheory.EulerInstantiation
decl_use
zetaReciprocal_local_factorization
in IndisputableMonolith.NumberTheory.EulerInstantiation
decl_use
LocalMeromorphicWitness
in IndisputableMonolith.NumberTheory.MeromorphicCircleOrder
decl_use