Geodesic
A criterion for the sequence of roots of holomorphic function with restrictions on its growth
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2020), pp. 55-61

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The main result of the paper is a criterion for a sequence of points in a domain of the complex plane, giving necessary and sufficient conditions under which this sequence of points is an exact sequence of zeros of some holomorphic function whose logarithm of modulus is majored by a given subharmonic function in the domain under consideration. Our criterion for the distribution of zeros of holomorphic functions with a given majorant is formulated in terms of special integral bounds and uses a new notion we recently introduced of affine balayage of measures. In one of our previous joint communications this criterion was announced without any proof. Here we fill this gap and give a criterion with exact definitions and a complete proof.
Keywords: holomorphic function, sequence of roots, balayage (sweeping out), subharmonic function, logarithmic potential. 
@article{IVM_2020_5_a4,
     author = {E. B. Menshikova and B. N. Khabibullin},
     title = {A criterion for the sequence of roots of holomorphic function with restrictions on its growth},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--61},
     publisher = {mathdoc},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_5_a4/}
}
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E. B. Menshikova; B. N. Khabibullin. A criterion for the sequence of roots of holomorphic function with restrictions on its growth. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2020), pp. 55-61. http://geodesic.mathdoc.fr/item/IVM_2020_5_a4/