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On the Exponent of Convergence for the Zeros of the Solutions of y~11 + Ay~' + By = 0

机译:y〜11 + Ay〜'+ By = 0解的零点的收敛指数

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摘要

It is assumed that the reader of this paper is familiar with the basic concepts of Nevanlinna theory [1, 2] such as T(r,f), m(r,f), N(r,f), and S(r,f). Suppose that / is a meromorphic function, then the order of growth of the function / and the exponent of convergence of the zeros of f/ are defined, respectively, as p(f) = lim sup log T(r,f)/log r, λ(f) = lim sup log N(r,1/f)/log r r → ∞ r → ∞.
机译:假定本文的读者熟悉Nevanlinna理论的基本概念[1,2],例如T(r,f),m(r,f),N(r,f)和S(r ,F)。假设/是亚纯函数,则将函数/的增长顺序和f /的零点的收敛指数分别定义为p(f)= lim sup log T(r,f)/ log r,λ(f)=极限值N(r,1 / f)/ log rr→∞r→∞。

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