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p-Adic Zeroes of the Kubota-Leopoldt Zeta-Function
Journal article   Peer reviewed

p-Adic Zeroes of the Kubota-Leopoldt Zeta-Function

Nof Alharbi, Rania Kammoun and Cenap Ozel
P-adic numbers, ultrametric analysis, and applications, Vol.11(4), pp.255-269
01/10/2019
DOI: https://doi.org/10.1134/S2070046619040010

Abstract

Mathematics Mathematics, Interdisciplinary Applications Physical Sciences Science & Technology
In this paper we establish why the p-adic zeta function has a Dirichlet series expansion. We compute an improved expansion, which allows us to express it as a power-series modulo p(n). Using this expansion, we compute all the zeros of L-p (s, chi(omega j)) for those quadratic characters chi of conductor < 200. For the calculation we use a PARI-GP Program.

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