Finding p-adic zeroes of the Kubota-Leopoldt zeta-function numerically
Alharbi, N. T. S. (2014). Finding p-adic zeroes of the Kubota-Leopoldt zeta-function numerically (Thesis, Master of Science (MSc)). University of Waikato, Hamilton, New Zealand. Retrieved from http://hdl.handle.net/10289/8692
Permanent Research Commons link: http://hdl.handle.net/10289/8692
We first establish why the p-adic zeta function has a Dirichlet series expansion. We then compute an improved expansion, which allows us to express it as a power-series modulo pⁿ. Using this expansion, we compute all the zeros of L₋p(s, χωʲ) for those quadratic characters χ of conductor < 200.
University of Waikato
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