On the existence of fixpoints of composite meromorphic functions

Bergweiler, Walter

doi:10.1090/S0002-9939-1992-1091176-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the existence of fixpoints of composite meromorphic functions
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by Walter Bergweiler

Proc. Amer. Math. Soc. 114 (1992), 879-880

DOI: https://doi.org/10.1090/S0002-9939-1992-1091176-X

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Abstract:

Let $f$ be a meromorphic function with at least two poles, and let $g$ be an entire transcendental function. It is proved that the composite function $f \circ g$ has infinitely many fixpoints.

References

Walter Bergweiler, Proof of a conjecture of Gross concerning fix-points, Math. Z. 204 (1990), no. 3, 381–390. MR 1107470, DOI 10.1007/BF02570881
Fred Gross, On factorization of meromorphic functions, Trans. Amer. Math. Soc. 131 (1968), 215–222. MR 220936, DOI 10.1090/S0002-9947-1968-0220936-0

Factorization of meromorphic functions