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The growth of solutions of algebraic differential equations

Walter K. Hayman — 1996

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Suppose that $f (z)$ is a meromorphic or entire function satisfying $P (z, f, f^{'}, \dots, f^{(n)}) = 0$ where $P$ is a polynomial in all its arguments. Is there a limitation on the growth of $f$ , as measured by its characteristic $T (r, f)$ ? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.

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