On the distribution of the zeros of the Riemann zeta function in short intervals (Q917589)
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scientific article; zbMATH DE number 4156559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the distribution of the zeros of the Riemann zeta function in short intervals |
scientific article; zbMATH DE number 4156559 |
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On the distribution of the zeros of the Riemann zeta function in short intervals (English)
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1990
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Let \(s(t)=(1/\pi)\arg \zeta (+it)\). Assuming the Riemann Hypothesis the author obtains an asymptotic formula for \(\int^{T}_{0}(s(t+\Delta)- s(t))^ 2dt\), where \(\Delta =o(1)\). The method is based on \textit{D. A. Goldston}'s paper [J. Number Theory 27, 149-177 (1987; Zbl 0618.10037)] and the result refines a previous result of the author [Bull. Am. Math. Soc. 81, 139-142 (1975; Zbl 0297.10026)].
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Riemann zeta function
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Riemann Hypothesis
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