The Gauss-Bonnet theorem and \(\zeta(2)\) (Q790151)
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scientific article; zbMATH DE number 3847480
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Gauss-Bonnet theorem and \(\zeta(2)\) |
scientific article; zbMATH DE number 3847480 |
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The Gauss-Bonnet theorem and \(\zeta(2)\) (English)
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1984
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The author calculates the volume of a fundamental domain for the modular group acting on the upper half plane in two different ways and obtains the well known result \(\zeta(2)=\pi^ 2/6\). One way is 'essentially' that of \textit{C. L. Siegel} [Am. J. Math. 65, 1-86 (1943; Zbl 0138.314)] and the other one uses Gauss-Bonnet theorem applied to a suitable cover of the fundamental domain, which is needed because of the presence of elliptic points for the full group.
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zeta(2)
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Riemann zeta-function
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volume
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fundamental domain
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modular group
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Gauss-Bonnet theorem
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0.7152097225189209
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0.7065293788909912
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0.6991659998893738
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