On the fourth weighted mean value formulas of Dirichlet \(L\)-functions (Q2719611)
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scientific article; zbMATH DE number 1609815
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the fourth weighted mean value formulas of Dirichlet \(L\)-functions |
scientific article; zbMATH DE number 1609815 |
Statements
25 June 2001
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asymptotic formula
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Gaussian sum
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Dirichlet's \(L\)-function
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0.90462863
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0.90449566
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0.9005592
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On the fourth weighted mean value formulas of Dirichlet \(L\)-functions (English)
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An asymptotic formula for the sum NEWLINE\[NEWLINE\sum_{q\leq Q} q/(\varphi(q))^{k+1} \sum_{\chi\neq\chi_0} |\tau(\chi)|^{2k} |L'(1,\chi)/ L(1,\chi)|^4,NEWLINE\]NEWLINE where \(\tau(\chi)\) is the Gaussian sum and \(L(s,\chi)\) is Dirichlet's \(L\)-function, is established.
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