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\(L\)-functions of \(p\)-adic characters. (English) Zbl 1292.11074

The authors define a \(p\)-adic character to be a continuous homomorphism from \(1+t\mathbb{F}_q[[t]]\) to \(\mathbb{Z}_p^*\). They give a correspondence between \(p\)-adic characters and sequences \((c_i)_{(i,p)=1}\) with \(c_i \in \mathbb{Z}_q\), such that \(c_i\) tends to zero.
The authors associate an \(L\)-function to \(p\)-adic characters and discuss the convergence of these \(L\)-series in terms of the corresponding sequence \((c_i)\).

MSC:

11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
13F35 Witt vectors and related rings
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References:

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