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Abstract

In this dissertation we deal with the distribution of zeros of special values of Goss zeta functions. Firstly, we prove an analogue of Riemann hypothesis for curves defined over prime field of arbitrary genus as well as for curves defined over \F_q with q\neq p whose genus is bounded by (p+q)/2. Secondly, we prove some results on partial zeta functions. Thirdly, we apply the cohomological method to a specified curve and prove an analogue of Riemann hypothesis for certain n. Finally, we set up a relation between the \infty-adic and v-adic zeta functions.