Resumen de Zeros of differences of meromorphic functions

Walter Bergweiler, James K. Langley

• Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = ?f(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.