On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order

V. I. Krutin'

Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 307-334

Résumé

In this paper analogues of results of W. K. Hayman and V. I. Petrenko for functions meromorphic in the finite complex plane are established. The results concern $p$-dimensional entire curves $\vec G(z)=\{g_n(z)\}_1^p$ (where the $g_n(z)$ are linearly independent integral functions). We show that $\sum_{\vec a\in A}\beta^\alpha(\vec a,\vec G)$ converges for $1\ge\alpha>1/2$ and $\sum_{\vec a\in A}\delta^\alpha(\vec a,\vec G)$ converges for $\alpha>1/3$, where $\beta(\vec a,\vec G)$ is the magnitude of the positive deviation of the integral curve, $\delta(\vec a,\vec G)$ the Nevanlinna defect and $A$ an admissible system of vectors. Bibliography: 18 titles.