Theorems · Theorem · complex analysis
ValueDistribution.characteristic_sub_characteristic_inv_at_zero
∀ {f : ℂ → ℂ},
Meromorphic f → ValueDistribution.characteristic f ⊤ 0 - ValueDistribution.characteristic f⁻¹ ⊤ 0 = Real.log ‖f 0‖Helper lemma for the first part of the First Main Theorem: At 0, the difference between the
characteristic functions of f and f⁻¹ equals log ‖f 0‖.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
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- Norm.normstatement and proof · cited by 5,413
- Set.univproof · cited by 3,945
- WithTopstatement · cited by 3,754
- Real.logstatement and proof · cited by 939
- sub_zeroproof · cited by 938
- Meromorphicstatement and proof · cited by 108
- Real.circleAverageproof · cited by 106
- MeromorphicOn.divisorproof · cited by 90
Cited by1
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_sub_characteristic_inv_leproof · cited by 1