Computing groups of Hecke characters

TL;DR

This paper presents algorithms for representing and computing groups of Hecke characters using an idelic approach, including methods to isolate algebraic characters, with implementation and examples in Pari/GP.

Contribution

It introduces new algorithms for computing and representing Hecke character groups, including algebraic and transcendental characters, with practical implementation.

Findings

Algorithms successfully compute Hecke character groups

Implementation in Pari/GP demonstrates practical applicability

Able to isolate algebraic characters effectively

Abstract

We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{\`e}lic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic characters, which are of particular interest in number theory. This work has been implemented in Pari/GP, and we illustrate our work with a variety of explicit examples using our implementation.