Degree bounds for algebra generators of invariant rings are a topic of
longstanding interest in invariant theory. We study the analogous question for
field generators for the field of rational invariants of a representation of a
finite group, focusing on abelian groups and especially the case of
Z/pZ. The inquiry is motivated by an application to signal
processing. We give new lower and upper bounds depending on the number of
distinct nontrivial characters in the representation. We obtain additional
detailed information in the case of two distinct nontrivial characters. We
conjecture a sharper upper bound in the Z/pZ case, and pose
questions for further investigation.Comment: 39 pages, 1 tabl