On the fourth power mean of Dirichlet L-functions (Q804624)
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scientific article; zbMATH DE number 4202389
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the fourth power mean of Dirichlet L-functions |
scientific article; zbMATH DE number 4202389 |
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On the fourth power mean of Dirichlet L-functions (English)
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1990
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The author uses an elementary method to prove the following asymptotic formula: \[ \sum_{\chi \neq \chi_ 0}| L(1,\chi)|^ 4=\frac{5\pi^ 4\phi (q)}{72}\prod_{p| q}\frac{(p^ 2-1)^ 3}{p^ 4(p^ 2+1)}+O(\exp (\frac{4 \log q}{\log \log q})), \] where the sum is over non-principal characters \(\chi\) mod q.
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fourth power mean
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Dirichlet L-functions
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asymptotic formula
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