Is D1Tuple — tail irregular and growth of four le
ProvedD1Bound5.IsD1Tuple.tail_irregular_and_growth_of_four_lediophantine-tuplesnumber-theory
The large-C tail lemma and its growth consequence for an actual ordered D(1) quadruple. Monotonicity allows equal moduli.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Data.Finset.Card import Mathlib.Data.Int.GCD import Mathlib.Data.Real.Basic import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_IsD1Tuple import Definitions.Def_D1Bound5_Regular_Definitions
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.IsD1Tuple.tail_irregular_and_growth_of_four_le
{K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
(hK : finrank ℚ K = 2) (phi : K →+* ℂ)
(t : Fin 4 → 𝓞 K) (ht : IsD1Tuple t)
(hmon : Monotone (fun i => ‖phi (t i : K)‖))
(hB : 3 ≤ ‖phi (t 1 : K)‖) (hC : 4 ≤ ‖phi (t 2 : K)‖) :
regularDefect (t 1) (t 2) (t 3) ≠ 0 ∧
2*‖phi (t 1 : K)‖*‖phi (t 2 : K)‖ < ‖phi (t 3 : K)‖ := by sorry
end D1Bound5
end
Source
D1Bound5/TailAnalyticMain.lean, lines 181-204, SHA-256 ecaba9e1e964c7e6c51088002aaaf592031aa2393ee6eb52d94273cfda86b389. Project: https://github.com/tomislav-math/d1-bound5-lean