Macdonald's Theorem for Analytic Functions

Abstract

A proof is reconstructed for a useful theorem on the zeros of derivatives of analytic functions due to H. M. Macdonald, which appears to be now little known. The Theorem states that, if a function $f(z)$ is analytic inside a bounded region bounded by a contour on which the modulus of $f(z)$ is constant, then the number of zeros (counted according to multiplicity) of $f(z)$ and of its derivative in the region differ by unity.

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Cited by in corpus (2)

• Arguments Related to the Riemann Hypothesis: New Methods and Results
• Sum Rules for Functions of the Riemann Zeta Type