# The Riemann Hypothesis for the Goss Zeta Function for Fq[T]☆

```@article{Sheats1998TheRH,
title={The Riemann Hypothesis for the Goss Zeta Function for Fq[T]☆},
author={Jeffrey T. Sheats},
journal={Journal of Number Theory},
year={1998},
volume={71},
pages={121-157}
}```
Letqbe a power of a primep. We prove an assertion of Carlitz which takesqas a parameter. Diaz-Vargas' proof of the Riemann Hypothesis for the Goss zeta function for Fp[T] depends on his verification of Carlitz's assertion for the specific caseq=p[D-V]. Our proof of the general case allows us to extend Diaz-Vargas' proof to Fq[T].

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