Mean-value of the Riemann zeta-function on the critical line (Q762541)
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scientific article; zbMATH DE number 3889650
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mean-value of the Riemann zeta-function on the critical line |
scientific article; zbMATH DE number 3889650 |
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Mean-value of the Riemann zeta-function on the critical line (English)
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1984
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In this expository article, the mean value of \(| \zeta (+it)|^{2k}\) is first discussed for \(k=1,2\), and 6, and then for arbitrary positive k. Results of the latter type are notably due to the authors and D. R. Heath-Brown. In conclusion, some results on weighted mean values are mentioned.
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Riemann zeta-function
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mean value
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critical line
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mean fourth power
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mean twelfth power
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0.9907658
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0.9647741
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0.95181346
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0.9501224
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0.9485842
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0.94430053
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0.9432819
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