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Mat. Zametki, 2018, Volume 103, Issue 4, Pages 490–502 (Mi mz11737)  

This article is cited in 5 scientific papers (total in 5 papers)

On Singular points of Meromorphic Functions Determined by Continued Fractions

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: It is shown that Leighton's conjecture about singular points of meromorphic functions represented by C-fractions $\mathscr K _{n=1}^\infty(a_nz^{\alpha_n}/1)$ with exponents $\alpha_1,\alpha_2,…$ tending to infinity, which was proved by Gonchar for a nondecreasing sequence of exponents, holds also for meromorphic functions represented by continued fractions $\mathscr K _{n=1}^\infty(a_nA_n(z)/1)$, where $A_1,A_2,…$ is a sequence of polynomials with limit distribution of zeros whose degrees tend to infinity.

Keywords: continued fraction, Hankel determinant, transfinite diameter, meromorphic continuation.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07531
Ministry of Education and Science of the Russian Federation НШ-9110.2016.1
This work was supported in part by the Russian Foundation for Basic Research under grant 15-01-07531 and by the program “Leading Scientific Schools” under grant NSh-9110.2016.1.


DOI: https://doi.org/10.4213/mzm11737

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English version:
Mathematical Notes, 2018, 103:4, 527–536

Bibliographic databases:

UDC: 517.53
Received: 06.07.2017

Citation: V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Mat. Zametki, 103:4 (2018), 490–502; Math. Notes, 103:4 (2018), 527–536

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v103/i4/p490

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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. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. I. Buslaev, “Schur's criterion for formal power series”, Sb. Math., 210:11 (2019), 1563–1580  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Math. Notes, 107:5 (2020), 701–712  mathnet  crossref  crossref  isi  elib
    4. V. I. Buslaev, “Schur's Criterion for Formal Newton Series”, Math. Notes, 108:6 (2020), 884–888  mathnet  crossref  crossref
    5. V. I. Buslaev, “Neobkhodimye i dostatochnye usloviya prodolzhimosti funktsii do funktsii Shura”, Matem. sb., 211:12 (2020), 3–48  mathnet  crossref
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