Coherent Retained Row — parameters
ProvedD1Bound5.CoherentRetainedRow.parametersdiophantine-tuplesnumber-theory
Auxiliary result CoherentRetainedRow.parameters 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.NatAntidiagonal import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Analytic.Binomial import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Insert import Mathlib.Data.Int.GCD import Mathlib.Data.Sym.Basic import Mathlib.Data.Sym.Card import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Lagrange import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.RingTheory.Binomial import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_CoherentRetainedMixedForms_Definitions import Definitions.Def_D1Bound5_CoherentThreeParameters_Definitions
Formal statement
section
open Finset
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.CoherentRetainedRow.parameters {H lam U : ℝ}
(hrow : CoherentRetainedRow H lam U) :
1 < H ∧ H ≤ 48 ∧ U ≤ 179/10 ∧
0 < coherentThreeLowerConstant H ∧ 0 < coherentThreeUpperConstant H ∧
100*coherentThreeUpperConstant H/99 < lam ∧
5 < 100/(201*coherentThreeUpperConstant H) ∧
100/(199*coherentThreeLowerConstant H) < U := by sorry
end D1Bound5
end
Source
D1Bound5/CoherentRetainedMixedForms.lean, lines 14-29, SHA-256 eb96a42cf210b66dfcce899bd150fc1582a3f153a19beef7c93531438f527556. Project: https://github.com/tomislav-math/d1-bound5-lean