An explicit upper bound for \(|L(1,\chi)|\) when \(\chi(2)=1\) and \(\chi\) is even (Q2833096)
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scientific article; zbMATH DE number 6653584
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An explicit upper bound for \(|L(1,\chi)|\) when \(\chi(2)=1\) and \(\chi\) is even |
scientific article; zbMATH DE number 6653584 |
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16 November 2016
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\(L\)-functions
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Dirichlet character
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quadratic field
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Gauss sums
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An explicit upper bound for \(|L(1,\chi)|\) when \(\chi(2)=1\) and \(\chi\) is even (English)
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Let \(\chi\) be an even, primitive Dirichlet character of conductor \(q > 1\), such that \(\chi(2) = 1\). The main result of the paper states that: NEWLINENEWLINENEWLINE\[NEWLINE| L(1, \chi)| \leq \frac{1}{2} \log q - 0.02012.NEWLINE\]NEWLINE NEWLINENEWLINENEWLINEA second result provides an upper bound for the class number of a real quadratic field of discriminant \(q > 1\), such that \(\chi(2) = 1\), namely: NEWLINE\[NEWLINEh(\mathbb Q(\sqrt{q})) \leq\frac{\sqrt{q}}{2}\left(1- \frac{1}{25 \log q}\right).NEWLINE\]
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