Revista Matemática Iberoamericana


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Volume 18, Issue 2, 2002, pp. 301–324
DOI: 10.4171/RMI/320

Published online: 2002-08-31

Nevanlinna theory, fuchsian functions and brownian motion windings

Jean-Claude Gruet[1]

(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