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A Dirichlet series expansion for the p-adic zeta-function

Part of: Arithmetic algebraic geometry Algebraic number theory: global fields

Published online by Cambridge University Press:  09 April 2009

Daniel Delbourgo
Daniel Delbourgo
Affiliation:
Department of Mathematics, University Park, Nottingham, England, NG7 2RD, e-mail: dd@maths.nott.ac.uk
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Abstract

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We prove that the p-adic zeta-function constructed by Kubota and Leopoldt has the Dirichlet series expansion Where the convergence of the first summation is for the p-adic topology. The proof of this formula relates the values of p(–s, ω1+σ) for s ∈ Zp, with a branch of the ‘sth-fractional derivative’, of a suitable generating function.

MSC classification

Secondary: 11R23: Iwasawa theory 11G55: Polylogarithms and relations with $K$-theory 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 2 , October 2006 , pp. 215 - 224
Copyright
Copyright © Australian Mathematical Society 2006

References

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