Zeros of differences of meromorphic functions

• Autores: Walter Bergweiler, James K. Langley
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 142, Nº 1, 2007, págs. 133-147
• Idioma: inglés
• DOI: 10.1017/s0305004106009777
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• Resumen

  • 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.