A Jensen-Rohrlich type formula for the hyperbolic 3-space

TL;DR

This paper derives a Jensen-Rohrlich type formula for automorphic functions on hyperbolic 3-space associated with the group PSL_2 of the ring of integers in a number field, advancing the understanding of automorphic forms in higher dimensions.

Contribution

It introduces a new Jensen-Rohrlich type formula specifically for automorphic functions on hyperbolic 3-space related to PSL_2(O_K), extending classical formulas to a higher-dimensional setting.

Findings

Established a Jensen-Rohrlich type formula for hyperbolic 3-space automorphic functions.

Connected the formula to the structure of PSL_2 groups over number rings.

Provided tools for further analysis of automorphic forms in three-dimensional hyperbolic geometry.

Abstract

In this article we give a Jensen-Rohrlich type formula for a certain class of automorphic functions on the hyperbolic 3-space for the group $\mathrm{PSL}_2(\mathcal{O}_K)$.