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arXiv · 1811.01337

On the Distribution of Zero Sets of Holomorphic Functions

B. N. Khabibullin·A. P. Rozit
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Abstract

Let $M$ be a subharmonic function with Riesz measure $\nu_M$ in a domain $D$ in the $n$-dimensional complex Euclidean space $\mathbb C^n$, and let $f$ be a nonzero function that is holomorphic in $D$, vanishes on a set ${\sf Z}\subset D$, and satisfies $|f| \leq \exp M$ on $D$. Then restrictions on the growth of $\nu_M$ near the boundary of $D$ imply certain restrictions on the area/volume of $\sf Z$. We give a quantitative study of this phenomenon in the subharmonic framework.

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B. N. Khabibullin, A. P. Rozit. 2018-11-04. On the Distribution of Zero Sets of Holomorphic Functions. https://doi.org/10.4213/faa3485

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