KnowraRouché's theoremLinked fromLinked fromThe 7 pages that link to Rouché's theorem, each with the reason it gives.All 7Related 6Compared with 1Complex analysisRelated: It provides a practical way to count zeros by comparison.Maximum modulus principleRelated: Its contour inequality and zero-count conclusion rely on maximum-modulus estimates.Residue theoremRelated: Its zero-counting conclusions are connected to the argument principle and residues.Winding numberRelated: It uses equality of boundary winding numbers to establish equal zero counts.Argument principleRelated: It uses the argument principle to compare the zeros of perturbed functions.Hurwitz's theoremRelated: Rouché's theorem turns local uniform convergence into preservation of zero counts near an alleged limit zero.Jensen's formulaCompared with: It counts zeros through boundary comparison, whereas Jensen's formula weights them by distance.