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

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 ÍØ-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

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/mz11737
• https://doi.org/10.4213/mzm11737
• 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
2. V. I. Buslaev, “Schur's criterion for formal power series”, Sb. Math., 210:11 (2019), 1563–1580
3. V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Math. Notes, 107:5 (2020), 701–712
4. V. I. Buslaev, “Schur's Criterion for Formal Newton Series”, Math. Notes, 108:6 (2020), 884–888
5. V. I. Buslaev, “Neobkhodimye i dostatochnye usloviya prodolzhimosti funktsii do funktsii Shura”, Matem. sb., 211:12 (2020), 3–48
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