The Riemann Hypothesis for the Goss Zeta Function for imageq[T] Original Research Article

Letqbe a power of a primep. We prove an assertion of Carlitz which takesqas a parameter. Diaz-Vargasʹ proof of the Riemann Hypothesis for the Goss zeta function for imagep[T] depends on his verification of Carlitzʹs assertion for the specific caseq=p[D-V]. Our proof of the general case allows us to extend Diaz-Vargasʹ proof to imageq[T].