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June, 2002 Nevanlinna theory, fuchsian functions and brownian motion windings
Jean-Claude Gruet
Rev. Mat. Iberoamericana 18(2): 301-324 (June, 2002).


Atsuji proposed some integrals along Brownian paths to study the Nevanlinna characteristic function $T(f,r)$ when $f$ is meromorphic in the unit disk $D$. We show that his criterion does not apply to the basic case when $f$ is a modular elliptic function. The divergence of similar integrals computed along the geodesic flow is also proved.


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Jean-Claude Gruet. "Nevanlinna theory, fuchsian functions and brownian motion windings." Rev. Mat. Iberoamericana 18 (2) 301 - 324, June, 2002.


Published: June, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1055.60077
MathSciNet: MR1949830

Primary: 30D35 , 30F45 , 60J65

Keywords: Brownian motion , geodesic flow , meromorphic functions , Nevanlinna theory

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 2 • June, 2002
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