Geodesic
Zeros of holomorphic functions of finite order in the polydisc
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 103-112 
P. L. Polyakov. Zeros of holomorphic functions of finite order in the polydisc. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 103-112. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Estimates are proved for the volume of the zero set of a holomorphic function of finite order in the polydisc. These estimates make it possible to solve a problem posed by Stoll: namely, to prove that $\operatorname{ord}M=\min\{\operatorname{ord}f\}$ for an analytic subset $M$ of codimension 1 in the polydisc $D^n$ and holomorphic functions $f$ having $M$ as zero set. Bibliography: 7 titles.

[1] Stoll W., Holomorphic functions of finite order in several complex variables, Conf. board of math. science. Reg. conf. series in math. 21, Amer. Math. Soc., Providence, 1974 | MR | Zbl

[2] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 | MR | Zbl

[3] Nevanlinna R., Eindeutige analytische Functionen, Springer-Verlag, Berlin, 1936 | Zbl

[4] Dzhrbashyan M. M., “K probleme predstavimosti analiticheskikh funktsii”, Soobscheniya In-ta matem. i mekhaniki AN ArmSSR, 2 (1948), 3–40

[5] Henkin G. M., Polyakov P. L., “Les zéros des fonctions holomorphes d'order fini dans le bidisque”, C. R. Acad. Sc. Paris. Ser. I, 298:1 (1984), 5–8 | MR | Zbl

[6] Charpentier Ph., Resolution de l'equation $\overline{\partial u}=f$ et application aux zéros des fonctions holomorphes dans le bidisque, Preprint, Universite de Bordeaux, 1984

[7] Lelong P., Fonctions plurisousharmoniques et formes differentielles positives, Gordon Breach, Paris, 1968 | MR | Zbl