An integral equation formulation of the Riemann hypothesis (Q1316454)
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scientific article; zbMATH DE number 515541
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An integral equation formulation of the Riemann hypothesis |
scientific article; zbMATH DE number 515541 |
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An integral equation formulation of the Riemann hypothesis (English)
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20 June 1994
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The author proves that the Riemann hypothesis holds if and only if the non-nuclear Hilbert-Schmidt integral operator on \(L^ 2(0,1)\), \[ [A \rho f](t)=\int^ 1_ 0 \rho (t/x) f(x) dx, \] where \(\rho\) is the fractional part function, is injective. Several spectral properties of the operator \(A \rho\) are established.
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spectral property
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integral operator
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Riemann hypothesis
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non-nuclear Hilbert-Schmidt operator
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