An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial (Q632281)
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scientific article; zbMATH DE number 5866013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial |
scientific article; zbMATH DE number 5866013 |
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An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial (English)
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15 March 2011
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Let \(A(s)=\sum_{m\leq M}a(m)m^{-s}\) be a Dirichlet polynomial, where \(M\geq 1\) and \(a(m)\in{\mathbb C}\). The authors prove an asymptotic formula for \(\int_T^{2T}\left|\zeta\left(\frac 12+it\right)A\left(\frac 12+it\right)\right|^2dt\) with an error term \(\ll M^{1+\varepsilon}\log^2T+M^{\frac 52+\varepsilon}T^{-\frac 14}\).
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Riemann zeta-function
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Dirichlet polynomial
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