A note on the values of \(p\)-adic \(q\)-\(L\)-functions. (Q2767905)
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scientific article; zbMATH DE number 1698741
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the values of \(p\)-adic \(q\)-\(L\)-functions. |
scientific article; zbMATH DE number 1698741 |
Statements
10 October 2002
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\(q\)-zeta function
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\(q\)-\(L\)-function
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\(p\)-adic interpolation
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Mazur measure
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A note on the values of \(p\)-adic \(q\)-\(L\)-functions. (English)
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Let \(h\) be a natural number. The \(h\)-extension of the \(q\)-zeta function is defined as NEWLINE\[NEWLINE \zeta_q^{(h)}(s)=\frac{1-s+h}{1-s}(q-1)\sum\limits_{n=1}^\infty \frac{q^{nh}}{[n]^{s-1}}+\sum\limits_{n=1}^\infty \frac{q^{nh}}{[n]^s}. NEWLINE\]NEWLINE This can be generalized to \(q\)-\(L\)-functions. The author constructs a \(p\)-adic interpolation of the latter by introducing and investigating an appropriate analog of the Mazur measure.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00006].
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