Revista Matemática Iberoamericana
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Published online: 2002-08-31
Nevanlinna theory, fuchsian functions and brownian motion windingsJean-Claude Gruet (1) Université de Caen, France
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.
Keywords: Nevanlinna theory, meromorphic functions, Brownian motion, geodesic flow
Gruet Jean-Claude: Nevanlinna theory, fuchsian functions and brownian motion windings. Rev. Mat. Iberoam. 18 (2002), 301-324. doi: 10.4171/RMI/320