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 . *) 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. 431–460DOI 10.2977/PRIMS/1195169663