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Mat. Sb., 2013, Volume 204, Number 5, Pages 67–108 (Mi msb8122)  

This article is cited in 4 scientific papers (total in 4 papers)

The most rapid possible growth of the maximum modulus of a canonical product of noninteger order with a prescribed majorant of the counting function of zeros

A. Yu. Popov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Asymptotically sharp estimates for the logarithm of the maximum modulus of a canonical product are obtained in the case when the counting function of zeros has a prescribed majorant, while the arguments of the zeros can be arbitrary.
Bibliography: 9 titles.

Keywords: entire function of finite order, proximate order, canonical product, maximum modulus of an entire function.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 8209


DOI: https://doi.org/10.4213/sm8122

Full text: PDF file (731 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:5, 683–725

Bibliographic databases:

UDC: 517.53
MSC: 30D15
Received: 29.03.2012

Citation: A. Yu. Popov, “The most rapid possible growth of the maximum modulus of a canonical product of noninteger order with a prescribed majorant of the counting function of zeros”, Mat. Sb., 204:5 (2013), 67–108; Sb. Math., 204:5 (2013), 683–725

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8122
  • http://mi.mathnet.ru/eng/msb/v204/i5/p67

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. S. Myshakov, “An Analog of the Valiron–Goldberg Theorem under a Restriction Condition on the Averaged Counting Function of Zeros”, Math. Notes, 96:5 (2014), 831–835  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. F. S. Myshakov, A. Yu. Popov, “A refinement of Gol'dberg's theorem on estimating the type with respect to a proximate order of an entire function of integer order”, Sb. Math., 206:12 (2015), 1771–1796  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
    4. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
  • Математический сборник Sbornik: Mathematics (from 1967)
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