Zeros of differences of meromorphic functions
نویسندگان
چکیده
منابع مشابه
Zeros of differences of meromorphic functions
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 . MSC 2000: 30D35.
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Let f be a function transcendental and meromorphic in the plane with lim inf r→∞ T (r, f) (log r)2 = 0. Let q ∈ C with |q| > 1. It is shown that at least one of the functions F (z) = f(qz)− f(z), G(z) = F (z) f(z) has infinitely many zeros. This result is sharp. MSC 2000: 30D35.
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2007
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004106009777