A Note on Zeta Measures over Function Fields Original Research Article

Let r be a power of a prime number p, imager be the finite field of r elements, and imager[T] be the polynomial ring over imager. As an analogue to the Riemann zeta function over image, Goss constructed the zeta function ζimager[T](s) over imager[T]. In order to study this zeta function, Thakur calculated the divided power series associated to the zeta measure μx on imager[T]v, where v is a finite place of imager(T). This paper calculates the divided power series associated to the zeta measure on imager[T]∞=imager[[image]] and expresses ζimager[T](s) by an integral of some locally analytic function.