Finitely generated ideals in the Nevanlinna class

TL;DR

This paper explores finitely generated ideals in the Nevanlinna class, establishing new results and contrasting their properties with those in the algebra of bounded analytic functions, including the stable rank.

Contribution

It provides new analogues of known results for $H^{ abla}$ and demonstrates that the stable rank of the Nevanlinna class exceeds 1, unlike in $H^{ abla}$.

Findings

Analogues to known results for $H^{ abla}$ established.

Stable rank of the Nevanlinna class is greater than 1.

Contrasts with properties of $H^{ abla}$.

Abstract

In this paper we investigate finitely generated ideals in the Nevanlinna class. We prove analogues to some known results for the algebra of bounded analytic functions $H^{\infty}$. We also show that, in contrast to the $H^{\infty}$-case, the stable rank of the Nevanlinna class is strictly bigger than 1.