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

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.
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