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Matematicheskie Zametki, 2019, Volume 105, Issue 3, Pages 364–374
DOI: https://doi.org/10.4213/mzm11804 (Mi mzm11804) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Bombieri Problem for Bounded Univalent Functions

V. G. Gordienkoa, D. V. Prokhorovab

a Saratov State University
b Petrozavodsk State University
Full-text PDF (456 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm11804
Abstract: Bombieri proposed to describe the structure of the sets of values of the initial coefficients of normalized conformal mappings of the disk in a neighborhood of the corner point corresponding to the Koebe function. The Bombieri numbers characterize the limit position of the support hyperplane passing through a critical corner point. In this paper, the Bombieri problem is studied for the class of bounded normalized conformal mappings of the disk, where the role of the Koebe function is played by the Pick function. The Bombieri numbers for a pair of two nontrivial initial coefficients are calculated.
Keywords: univalent function, Bombieri number, Koebe function, Pick function.
Funding agency Grant number
Russian Science Foundation 17-11-01229
The work of the second author was supported by the Russian Science Foundation under grant 17-11-01229.
Received: 20.09.2017
English version:
Mathematical Notes, 2019, Volume 105, Issue 3, Pages 342–350
DOI: https://doi.org/10.1134/S0001434619030040
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. G. Gordienko, D. V. Prokhorov, “The Bombieri Problem for Bounded Univalent Functions”, Mat. Zametki, 105:3 (2019), 364–374; Math. Notes, 105:3 (2019), 342–350
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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