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

Nof Alharbi; Rania Kammoun; Cenap Ozel

doi:10.1134/S2070046619040010

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

作者: Alharbi N.¹, Kammoun R.², Ozel C.¹
隶属关系:
1. KAU King Abdulaziz University
2. University of Harf Al Batin, College of Sciences, Departement of Mathematics
期: 卷 11, 编号 4 (2019)
页面: 255-269
栏目: Research Articles
URL: https://journals.rcsi.science/2070-0466/article/view/201270
DOI: https://doi.org/10.1134/S2070046619040010
ID: 201270

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详细

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 pⁿ. Using this expansion, we compute all the zeros of L_p(s, χω^j) for those quadratic characters χ of conductor < 200. For the calculation we use a PARI-GP Program.