On some averages at the zeros of the derivatives of the Riemann zeta-function (Q555296)
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scientific article; zbMATH DE number 5931166
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some averages at the zeros of the derivatives of the Riemann zeta-function |
scientific article; zbMATH DE number 5931166 |
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On some averages at the zeros of the derivatives of the Riemann zeta-function (English)
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22 July 2011
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Assume that \(\rho_k\) denotes a non-real zero of the \(k\)-th derivative \(\zeta^{(k)}\) and \(\gamma_k=\Im(\rho_k)\). Moreover, let \(\chi(s)=2(2\pi)^{s-1}\Gamma(1-s)\sin(s\pi/2)\) be factor in the functional equation of the Riemann zeta-function. In the paper under review, the authors compute the averages \(\sum_{0<\gamma_k<T}\chi(\rho_k)\) and \(\sum_{0<\gamma_k\leq T}\zeta^{(k)}(\rho_k)\).
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Riemann zeta-function
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derivative of the Riemann zeta-function
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average
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