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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 6, Pages 5–42 (Mi izv8420)  

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

Nuttall's Abelian integral on the Riemann surface of the cube root of a polynomial of degree 3

A. I. Aptekarev*, D. N. Tulyakov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: We study the field of orthogonal trajectories of a quadratic differential on the three-sheeted Riemann surface of the cube root of a polynomial of degree 3. These trajectories coincide globally with the level lines of the velocity potential of an incompressible fluid flowing to the surface through the infinitely remote point on one sheet and flowing out through the infinitely remote point on another. The statement of the problem is motivated by the task of finding the distribution of the poles of the Hermite–Padé approximants for two analytic functions with three common branch points, which is in its turn related to Nuttall's general conjecture.

Keywords: algebraic functions, Riemann surfaces, trajectories of quadratic differentials, Hermite–Padé approximants.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025
This work was supported by the Russian Science Foundation under grant no. 14-21-00025.

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8420

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English version:
Izvestiya: Mathematics, 2016, 80:6, 997–1034

Bibliographic databases:

UDC: 517.53
MSC: 30B40, 30F30, 31A15, 41A21
Received: 17.06.2015
Revised: 31.01.2016

Citation: A. I. Aptekarev, D. N. Tulyakov, “Nuttall's Abelian integral on the Riemann surface of the cube root of a polynomial of degree 3”, Izv. RAN. Ser. Mat., 80:6 (2016), 5–42; Izv. Math., 80:6 (2016), 997–1034

Citation in format AMSBIB
\by A.~I.~Aptekarev, D.~N.~Tulyakov
\paper Nuttall's Abelian integral on the Riemann surface of the cube root of a~polynomial of degree~3
\jour Izv. RAN. Ser. Mat.
\yr 2016
\vol 80
\issue 6
\pages 5--42
\jour Izv. Math.
\yr 2016
\vol 80
\issue 6
\pages 997--1034

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    This publication is cited in the following articles:
    1. Martinez-Finkelshtein A., Silva G.L.F., “Spectral Curves, Variational Problems and the Hermitian Matrix Model With External Source”, Commun. Math. Phys.  crossref  isi
    2. A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.  mathnet  crossref
    4. V. G. Lysov, D. N. Tulyakov, “On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix”, Proc. Steklov Inst. Math., 298 (2017), 170–200  mathnet  crossref  crossref  isi  elib
    5. A. V. Komlov, “Polinomialnaya $m$-sistema Ermita–Pade dlya meromorfnykh funktsii na kompaktnoi rimanovoi poverkhnosti”, Matem. sb., 212:12 (2021), 40–76  mathnet  crossref
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