arXiv subjects
Publications and source records attributed to J. K. Langley.
We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.
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) or g(z)/f(z), in terms of the growth and the poles of f.
If f is a real entire function and ff" has only real zeros then f belongs to the Laguerre-Polya class, the closure of the set of real polynomials with real zeros. This result completes a long line of development originating from a conjecture of Wiman in 1914.