Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sum Expressions for Kubota-Leopoldt $p$-adic $L$-functions   When $p$ is an odd prime, Delbourgo observed that any Kubota-Leopoldt
$p$-adic $L$-function, when multiplied by an auxiliary Euler factor, can be
written as an infinite sum. We shall establish such expressions without
restriction on $p$, and without the Euler factor when the character is
nontrivial, by computing the periods of appropriate measures. As an
application, we will reprove the Ferrero-Greenberg formula for the derivative
$L_p'(0,\chi)$. We will also discuss the convergence of sum expressions in
terms of elementary $p$-adic analysis, as well as their relation to
Stickelberger elements; such discussions in turn give alternative proofs of the
validity of sum expressions.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: stat