Growth of analytic functions in an ultrametric open disk and branched values

نویسندگان

چکیده

Let $D$ be the open disk $|x|< R$ of a complete ultrametric algebraically closed field $\mathbb K$. We define growth order $\rho(f)$, type $\sigma(f)$ cotype $\psi(f)$ and another expression $\theta(f)$ an analytic function in we show relations between number zeros $f$ ``maximum modulus'' involving $\rho,\sigma,\psi$. Then $\rho(f)$ lies $[\theta(f)-1, \theta(f)]$. Moreover, if $0< \rho(f)< +\infty$ \psi(f)< +\infty$, then $\theta(f)=\rho(f)$ $\sigma(f)=0$. Suppose K$ has characteristic zero consider two unbounded functions $f,g$ $D$. The perfectly branched values admits overbounds linked to $\rho(f), \rho(g), \sigma(f), \sigma(g)$. In residue zero, $\rho(f')=\rho(f),\sigma(f')=\sigma(f),$ $ \psi(f')=\psi(f)$, which can applied Levi-Civta fields.

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ژورنال

عنوان ژورنال: Simon Stevin

سال: 2021

ISSN: ['1370-1444', '2034-1970']

DOI: https://doi.org/10.36045/j.bbms.200707