Universality of the Selberg zeta-function for the modular group (Q2836445)
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scientific article; zbMATH DE number 6183136
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Universality of the Selberg zeta-function for the modular group |
scientific article; zbMATH DE number 6183136 |
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3 July 2013
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universality theorem
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Selberg zeta-function
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generalized Dirichlet series
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Universality of the Selberg zeta-function for the modular group (English)
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The first result on universality for the Riemann zeta-function \(\zeta(s)\), \(s=\sigma+it\), was obtained by \textit{S. M. Voronin} [Izv. Akad. Nauk SSSR, Ser. Mat. 39, 475--486 (1975; Zbl 0315.10037)]. In this paper, it is proved that the Selberg zeta-function \(Z(s)\) for the modular group \(\mathrm{SL}(2,\mathbb Z)\) is universal in Voronin's sense in the strip \(0.848... <\sigma<1\).NEWLINENEWLINEIt is important to mention that this result gives a first example of the universality property for the zeta-function of order 2.
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