Zeros of differences of meromorphic functions

By Walter Bergweiler, J. Langley. Mathematical Proceedings of the Cambridge Philosophical Society, 2005

201 citations recorded by the source corpus.

Abstract Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f. The results may be viewed as discrete analogues of existing theorems on the zeros of f' and f'/f.

Subfields: Applied Mathematics, Geometry and Topology

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Citations in the corpus

• Value distribution of the difference operator (2009, background): “Bergweiler and Langley [2] considered the value distribution of zeros of difference operators that can be viewed as discrete analogues of the zeros of f ′(z).”