Delbourgo, DanielAlharbi, Nof Turki S2014-08-012014-08-012014Alharbi, 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 https://hdl.handle.net/10289/8692https://hdl.handle.net/10289/8692We 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.application/pdfenAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.zeroes of p-adic L-functionThesis2014-03-12