Zeta Measure Associated to lF,[T]

The object of this paper is to identify the divided power series corresponding to the zeta measure associated to f f ,,[ r]. The first section introduces the zeta function for JF4[ T] and describes some of its interesting properties. In the second section, we describe results on interpolations and measures and state our main result (Theorem VII). The third section summarizes various results about power sums and zeta functions. The last section contains two proofs of the main result. In the appendix, we elaborate on the existence of zeta and beta measures and give alternate descriptions for them. t j 1990 Academic Press. Inc.