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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 292, Pages 92–119 (Mi znsl1668)  
This article is cited in 4 scientific papers (total in 4 papers)

Counting meromorphic functions with critical points of large multiplicities

D. Panova, D. Zvonkineb

a Ècole Polytechnique
b Paris-Sud University 11
Full-text PDF (345 kB) Citations (4)
Abstract: We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values.
When the Riemann surface is $\mathbb CP^1$ and the function is a polynomial, we give an elementary way of finding this number.
In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotics for the number of meromorphic functions is given by the volume of some space of graphs glued from circles. We express this volume as a matrix integral.
Received: 27.09.2002
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 126, Issue 2, Pages 1095–1110
DOI: https://doi.org/10.1007/s10958-005-0095-1
Bibliographic databases:
UDC: 519.11+517.98
Language: English
Citation: D. Panov, D. Zvonkine, “Counting meromorphic functions with critical points of large multiplicities”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VII, Zap. Nauchn. Sem. POMI, 292, POMI, St. Petersburg, 2002, 92–119; J. Math. Sci. (N. Y.), 126:2 (2005), 1095–1110
Citation in format AMSBIB
\Bibitem{PanZvo02}
\by D.~Panov, D.~Zvonkine
\paper Counting meromorphic functions with critical points of large multiplicities
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~VII
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 292
\pages 92--119
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1668}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1944086}
\zmath{https://zbmath.org/?q=an:1086.30039}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 126
\issue 2
\pages 1095--1110
\crossref{https://doi.org/10.1007/s10958-005-0095-1}
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  • https://www.mathnet.ru/eng/znsl/v292/p92
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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