Some mean squares in connection with \(\zeta(1+it)\) (Q1318932)
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scientific article; zbMATH DE number 549031
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some mean squares in connection with \(\zeta(1+it)\) |
scientific article; zbMATH DE number 549031 |
Statements
Some mean squares in connection with \(\zeta(1+it)\) (English)
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20 November 1994
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The author proves that \[ \int_ 1^ T | \zeta^{(\nu)} (1+it)|^ 2 dt= \zeta^{(2\nu)} (2)T+ O(\log^{2\nu+1} T) \qquad (\nu\geq 1 \text{ fixed}) \] and states several other asymptotic formulas involving \(\zeta (1+ it)\). As mentioned by him in the text, the author's results follow (some with even sharper error terms) from a general theorem by \textit{R. Balasubramanian}, \textit{K. Ramachandra} and the reviewer [Acta Arith. 65, 45-51 (1993; Zbl 0781.11035)].
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Riemann zeta-function
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mean values
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Montgomery-Vaughan theorem
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approximate functional equation
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asymptotic formulas
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