A Dedekind-Rademacher cocycle for Bianchi groups

TL;DR

This paper generalizes the Dedekind-Rademacher cocycle to Bianchi groups, explores its properties, and links it to $L$-values, establishing their integrality.

Contribution

It introduces a new cocycle for Bianchi groups, extending classical concepts and connecting them to special $L$-values with integrality results.

Findings

Constructed a generalized Dedekind-Rademacher cocycle for Bianchi groups.

Showed the cocycle parametrizes a family of $L$-values.

Proved the integrality of these $L$-values.

Abstract

We construct a generalization of the Dedekind-Rademacher cocycle to congruence subgroups of $\mathrm{SL}_2(\mathbb C)$, and derive some of its basic properties. In particular, we show that it parametrizes a family of $L$-values and prove the integrality of these values.