Eichler Cohomology of Generalized Modular Forms of Real Weights

TL;DR

This paper proves an Eichler cohomology theorem for generalized modular forms of real weights, establishing an explicit isomorphism between cusp forms and cohomology groups for large weights.

Contribution

It extends Eichler cohomology to weakly parabolic generalized modular forms of real weights and constructs explicit isomorphisms for large weights.

Findings

Established Eichler cohomology theorem for real weights

Constructed explicit isomorphism for large weights

Extended classical theory to generalized modular forms

Abstract

In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by constructing the map from the space of cusp forms to the cohomology group.