Finite Q half coefficients

Proved

D1Bound5.finiteQ_half_coefficients

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finiteQ_half_coefficients in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_HalfBinomialCoefficients_Definitions

Formal statement

section
open Finset

namespace D1Bound5

theorem _root_.D1Bound5.finiteQ_half_coefficients :
    halfBinomialCoeff 0 = 1 ∧ halfBinomialCoeff 1 = 1/2 ∧
    halfBinomialCoeff 2 = -1/8 ∧ halfBinomialCoeff 3 = 1/16 ∧
    halfBinomialCoeff 4 = -5/128 := by sorry









end D1Bound5
end

Source

D1Bound5/FiniteQResidualIdentity.lean, lines 9-28, SHA-256 74ab040376af9b42e7ee62656f2fd8f3a92a0111248e8b31465d43a74a137c58. Project: https://github.com/tomislav-math/d1-bound5-lean

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