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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 6, Pages 1255–1261
DOI: https://doi.org/10.17377/smzh.2016.57.605 (Mi smj2821) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The logarithmic energy of zeros and poles of a rational function

V. N. Dubininab

a Far-Eastern Federal University, Vladivostok, Russia
b Institute of Applied Mathematics, Vladivostok, Russia
Full-text PDF (294 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2016.57.605
Abstract: On assuming that certain lemniscates of a rational function are connected, we establish some sharp inequality that involves the logarithmic energy of a discrete charge concentrated at the zeros and poles of this function and the absolute values of its derivatives at these points. The equality in this estimate is attained for specially arranged zeros and poles of a suitable Zolotarev fraction and for special distributions of charge.
Keywords: rational function, Zolotarev fraction, lemniscate, logarithmic energy.
Funding agency Grant number
Russian Science Foundation 14-11-00022
The author was supported by the Russian Science Foundation (Grant 14-11-00022).
Received: 26.04.2016
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 6, Pages 981–986
DOI: https://doi.org/10.1134/S0037446616060057
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “The logarithmic energy of zeros and poles of a rational function”, Sibirsk. Mat. Zh., 57:6 (2016), 1255–1261; Siberian Math. J., 57:6 (2016), 981–986
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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