Finite PHalf Remainder norm le
ProvedD1Bound5.finitePHalfRemainder_norm_lediophantine-tuplesnumber-theory
Degree-six tail estimate for the actual principal half power.
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.FinCases import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_FiniteQResidualIdentity_Definitions
Formal statement
section
open Finset
namespace D1Bound5
attribute [local simp] Matrix.cons_val_two Matrix.cons_val_three
theorem _root_.D1Bound5.finitePHalfRemainder_norm_le (n : ℕ) (z : ℂ)
(hn : 6 ≤ n) (hz : ‖z‖ < 1) :
‖finiteQHalfRemainder n z‖ ≤ (21/1024 : ℝ)*‖z‖^n/(1-‖z‖) := by sorry
end D1Bound5
end
Source
D1Bound5/FinitePResidualIdentity.lean, lines 29-62, SHA-256 72e3fea4ae1d93b79c83366074679f850f075659fb82a9a62794934f87487052. Project: https://github.com/tomislav-math/d1-bound5-lean