Theorems · Theorem · complex analysis
Complex.canonicalFactor_ne_zero
∀ {R : ℝ} {w z : ℂ}, w ∈ Metric.ball 0 R → z ∈ Metric.closedBall 0 R → z ≠ w → Complex.canonicalFactor R w z ≠ 0The canonical factor CanonicalFactor R w has no zeros inside the ball of radius R.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- le_reflproof · cited by 2,061
- Complex.ofRealproof · cited by 1,654
- Metric.ballstatement and proof · cited by 735
- norm_nonnegproof · cited by 725
- Metric.closedBallstatement and proof · cited by 704
- starRingEndproof · cited by 671
- ne_of_gtproof · cited by 637
Cited by6
Results whose statement or proof uses this declaration.
- MeromorphicOn.exists_canonicalDecompproof · cited by 1
- Complex.CanonicalDecomp.divisor_eq_divisorproof · cited by 1
- Complex.divisor_canonicalFactorproof · cited by 0
- Complex.ECanonicalDecomp.log_norm_eqproof · cited by 0
- Complex.canonicalFactor_eq_zero_iffproof · cited by 0