On the type of the meromorphic function of finite order

M. V. Kabanko

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 212-224

Résumé

Let $f(z)$ be a meromorphic function on the complex plane of finite order $\rho>0$. Let $\rho(r)$ be a proximate order in the sense of Boutroux such that $\limsup\limits_{r\to\infty}\rho(r)=\rho$, $\liminf\limits_{r\to\infty}\rho(r)=\alpha>0$. If $[\alpha]\alpha\leqslant\rho[\alpha]+1$ then the types of $T(r,f)$ and $|N|(r,f)$ coincide with respect to $\rho(r)$. If there are integers between $\alpha$ and $\rho$, then the resulting criterion is formulated in terms of the upper density of zeros and poles of the function $f$ and their argument symmetry.

Détail

Keywords: meromorphic function, function order, function type, upper density, argument symmetry.