The remainder terms aspect of the theory of the Riemann zeta function (Q1183124)
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scientific article; zbMATH DE number 32731
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The remainder terms aspect of the theory of the Riemann zeta function |
scientific article; zbMATH DE number 32731 |
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The remainder terms aspect of the theory of the Riemann zeta function (English)
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28 June 1992
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The paper produces a number of relationships between \(R(x)\) and \(S(T)\), these being the remainder terms for \(\psi(x)\) and \(N(T)\) respectively. All the results assume the Riemann Hypothesis. The precise formulae are too complicated to state here, but they express fractional integrals of \(R(x)\) (in the sense of Riemann and Liouville) as suitable transforms of \(S(T)\). The results may be seen as extensions of Guinand's formula.
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remainder terms
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Riemann Hypothesis
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fractional integrals
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extensions of Guinand's formula
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Riemann zeta-function
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zero counting formula
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prime number theorem
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