Geodesic
On the Distribution of Zero Sets of Holomorphic Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 26-42

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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 ${\mathsf Z}\subset D$, and satisfies $|f|\le \exp M$ on $D$. Then restrictions on the growth of $\nu_M$ near the boundary of $D$ imply certain restrictions on the dimensions or the area/volume of $\mathsf Z$. We give a quantitative study of this phenomenon in the subharmonic framework.
Keywords: holomorphic function, zero set, subharmonic function, Riesz measure, Jensen measure. 
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     author = {B. N. Khabibullin and A. P. Rozit},
     title = {On the {Distribution} of {Zero} {Sets} of {Holomorphic} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     number = {1},
     year = {2018},
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B. N. Khabibullin; A. P. Rozit. On the Distribution of Zero Sets of Holomorphic Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 26-42. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a2/