Linked from

The 11 pages that link to Argument principle, each with the reason it gives.

• Complex analysisRelated: It counts roots without solving for them individually.

• Fundamental theorem of algebraRelated: It counts polynomial roots inside a large circle from the boundary’s winding.

• Meromorphic functionRelated: It counts zeros and poles of meromorphic functions using boundary values.

• Residue theoremRelated: It applies the residue theorem to the logarithmic derivative of a meromorphic function.

• Winding numberRelated: The theorem identifies this integer with the number of zeros minus poles enclosed by a complex contour.

• Cauchy's integral theoremRelated: It combines contour integration with zero integrals to count zeros and poles.

• Nyquist stability criterionRelated: It mathematically justifies counting closed-loop poles through encirclements.

• Rouché's theoremRelated: Rouché's theorem follows by applying this principle to a continuous family of functions.

• Hurwitz's theoremRelated: It explains why a small boundary perturbation cannot change the zero count used in Hurwitz's theorem.

• Jensen's formulaRelated: It is another contour-based method for extracting information about zeros from boundary behavior.

• Riemann–von Mangoldt formulaRelated: A contour integral of the zeta function’s logarithmic derivative yields the zero count.