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On the zero Distribution of Special Values of Goss zeta Functions

Qiu, Yujia

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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.

Item Type: Dissertation
Supervisor: Böckle, Prof. Dr. Gebhard
Date of thesis defense: 10 June 2016
Date Deposited: 17 Jun 2016 07:44
Date: 2016
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
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