415 citations · 1.2k across the 61 of their papers we have counts for
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Permutable entire functions satisfying algebraic differential equations
Walter Bergweiler
It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.
Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions
Walter Bergweiler, Alexandre Eremenko
We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tend…
Fixed points of composite entire and quasiregular maps
Walter Bergweiler
We give a new proof of the result that if f and g are transcendental entire functions, then the composite function f(g) has infinitely many fixed points. The method yields a number…
Zeros of differences of meromorphic functions
Walter Bergweiler, J. K. Langley
Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) o…