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Degree bounds for algebra generators of invariant rings are a topic oflongstanding interest in invariant theory. We study the analogous question forfield generators for the field of rational invariants of a representation of afinite group, focusing on abelian groups and especially the case of$\mathbb{Z}/p\mathbb{Z}$. The inquiry is motivated by an application to signalprocessing. We give new lower and upper bounds depending on the number ofdistinct nontrivial characters in the representation. We obtain additionaldetailed information in the case of two distinct nontrivial characters. Weconjecture a sharper upper bound in the $\mathbb{Z}/p\mathbb{Z}$ case, and posequestions for further investigation.

Degree bounds for fields of rational invariants of $\mathbb{Z}/p\mathbb{Z}$ and other finite groups