Communications in Number Theory and Physics

Volume 15 (2021)

Number 3

Rational $2$-functions are abelian

Pages: 605 – 614



L. Felipe Müller (Mathematisches Institut, Universität Heidelberg, Germany)


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.

2010 Mathematics Subject Classification

Primary 30C10, 81Q60. Secondary 33B30.

Received 9 March 2021

Accepted 1 May 2021

Published 15 July 2021