Nevanlinna theory, fuchsian functions and brownian motion windings

  • Jean-Claude Gruet

    Université de Caen, France

Abstract

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

Cite this article

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