J. Aust. Math. Soc.
81 (2006), 215224

A Dirichlet series expansion for the padic zetafunction

Daniel Delbourgo
Department of Mathematics
University Park
Nottingham
England NG7 2RD
dd@maths.nott.ac.uk



Abstract

We prove that the
padic zetafunction constructed by Kubota and
Leopoldt has the Dirichlet series expansion


where the convergence of the first summation is
for the
padic topology. The proof of this formula relates
the values of
for
, with a branch of the
`fractional derivative' of a suitable generating
function.

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