Mean-value theorem of Riemann zeta-function over short intervals (Q1310835)
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scientific article; zbMATH DE number 483992
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mean-value theorem of Riemann zeta-function over short intervals |
scientific article; zbMATH DE number 483992 |
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Mean-value theorem of Riemann zeta-function over short intervals (English)
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9 May 1994
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Assuming the Riemann hypothesis, the authors obtain an asymptotic formula for the mean-square of \(\zeta(\sigma+it)\) over \((T,T+H)\), provided \(1/2+ c/\log\log T\leq\sigma\leq 1-\delta\) and \(Y\leq H\leq T\), where \(Y=\exp((\log T)^{2-2\sigma})\) and \(c,\delta>0\). The proof is based on a mean-value theorem for Dirichlet polynomials.
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asymptotic formula
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mean-square of Riemann zeta-function
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mean-value theorem
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Dirichlet polynomials
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