On \(\hat{\mathbb{Z}}\)-Zeta Function

Conference paper
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 7)


We present in this note a definition of zeta function of the field \(\mathbb{Q}\) which incorporates all p-adic L-functions of Kubota-Leopoldt for all p and also so called Soulé classes of the field \(\mathbb{Q}\). This zeta function is a measure, which we construct using the action of the absolute Galois group \(G_{\mathbb{Q}}\) on fundamental groups.


Fundamental Group Zeta Function Elliptic Curve Elliptic Curf Galois Group 
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These research were started in January 2011 during our visit in Max-Planck-Institut für Mathematik in Bonn. We would like to thank very much MPI for support. We would like also thank to Professor C. Greither for invitation on the conference Iwasawa 2008 in Kloster Irsee. We acknowledge the financial help of the Laboratoire de Dieudonné, which allows us to participate in the meeting Iwasawa 2012 in Heidelberg.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratoire Jean Alexandre Dieudonné, U.R.A. au C.N.R.S., No 168, Département de MathématiquesUniversité de Nice-Sophia AntipolisNice Cedex 2France

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