Rational 2-functions are abelian

TL;DR

This paper proves that the coefficients of rational 2-functions are contained in abelian number fields, with poles at roots of unity and rational residues, revealing their algebraic structure.

Contribution

It establishes that rational 2-functions have poles only at roots of unity with rational residues, showing their coefficients lie in abelian number fields.

Findings

Coefficients are in abelian number fields.

Poles are roots of unity with order one.

Residues are rational.

Abstract

We show that the coefficients of rational 2-functions are contained in an abelian number field. More precisely, we show that the poles of such functions are poles of order one and given by roots of unity and rational residue.