Geodesic
Distribution of zeros of functions with exponential growth
Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 355-363

Voir la notice de l'article provenant de la source Math-Net.Ru

For systems of equations with an infinite number of roots one can sometimes establish results of the type of the Kushnirenko–Bernstein–Khovanskii theorem by replacing the calculation of the number of the roots by the calculation of the asymptotic density of these roots. We consider systems of entire functions with exponential growth in $\mathbb C^n$ and calculate the asymptotic behaviour of the averaged distribution of their zeros in terms of the geometry of convex bodies in a complex vector space. Bibliography: 11 titles.
Keywords: Kushnirenko–Bernstein–Khovanskii theorem, Newton polytopes, zeros of holomorphic functions, exponential sums. 
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     author = {B. Ya. Kazarnovskii},
     title = {Distribution of zeros of functions with exponential growth},
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     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_3_a3/}
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B. Ya. Kazarnovskii. Distribution of zeros of functions with exponential growth. Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 355-363. http://geodesic.mathdoc.fr/item/SM_2024_215_3_a3/