On a factorization of Riemann's \(\zeta\) function with respect to a quadratic field and its computation (Q1935072)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a factorization of Riemann's \(\zeta\) function with respect to a quadratic field and its computation |
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On a factorization of Riemann's \(\zeta\) function with respect to a quadratic field and its computation (English)
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30 January 2013
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Let \(\chi\) be a quadratic Dirichlet character associated to a quadratic field. The author considers the functions \(p_1(s)=\prod_{\chi(p)=1}(1-p^{-s})^{-1}\) and \(p_2(s)=\prod_{\chi(p)=-1}(1-p^{-s})^{-1}\), shows their relations to \(\zeta(s)\) and \(L(s,\chi)\), and obtains fast converging series for their logarithms.
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Riemann \(\zeta\)-function
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functional equations
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quadratic fields
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factorization
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