On the value-distribution of Epstein zeta-functions (Q1021040)
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scientific article; zbMATH DE number 5562423
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the value-distribution of Epstein zeta-functions |
scientific article; zbMATH DE number 5562423 |
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On the value-distribution of Epstein zeta-functions (English)
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5 June 2009
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The paper is devoted to the investigation of the value-distribution of Epstein zeta-functions \(\zeta(s;{\mathcal Q})\) (\({\mathcal Q}\) is a positive definite quadratic form in \(n\) variables). It is proved the asymptotic formula for the number of \(c\)-values (the roots of the equation \(\zeta(s;{\mathcal Q})=c\) with fixed complex number \(c\)), and that these \(c\)-values have an asymmetric distribution with respect to the critical line \(\text{Re}\,s=n/4\).
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Epstein zeta-functions
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quadratic forms
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value-distribution
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Nevanlinna theory
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