# A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces

### Kyoji Saito

Kyoto University, Japan

## Abstract

Let (*X*, _KX_1/2) be a spin Riemann surface*) of genus ≥ 2. By using infinite dimensional representations of the fundamental group of *X*, we obtain many local systems on *X*, which taken together define *a resolution of the halfcanonical ring of X* and indicate a *non-abelian theory of abelian integrals on X*. The work has a root in a study of the complex structure on the Fricke moduli space [14]. *) a Riemann surface together with a halfcanonical bundle (4.1).

## Cite this article

Kyoji Saito, A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces. Publ. Res. Inst. Math. Sci. 27 (1991), no. 3, pp. 431–460

DOI 10.2977/PRIMS/1195169663