JournalsrmiVol. 18, No. 2pp. 301–324

Nevanlinna theory, fuchsian functions and brownian motion windings

  • Jean-Claude Gruet

    Université de Caen, France
Nevanlinna theory, fuchsian functions and brownian motion windings cover
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Abstract

Atsuji proposed some integrals along Brownian paths to study the Nevanlinna characteristic function T(f,r)T(f,r) when ff is meromorphic in the unit disk DD. We show that his criterion does not apply to the basic case when ff 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. Iberoam. 18 (2002), no. 2, pp. 301–324

DOI 10.4171/RMI/320