Explicit form of the hyperbolic term in the Selberg trace formula for \(Sl(3,{\mathbb{Z}})\) and Pell's equation for hyperbolics in \(Sl(3,{\mathbb{Z}})\) (Q1078233)
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scientific article; zbMATH DE number 3959543
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Explicit form of the hyperbolic term in the Selberg trace formula for \(Sl(3,{\mathbb{Z}})\) and Pell's equation for hyperbolics in \(Sl(3,{\mathbb{Z}})\) |
scientific article; zbMATH DE number 3959543 |
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Explicit form of the hyperbolic term in the Selberg trace formula for \(Sl(3,{\mathbb{Z}})\) and Pell's equation for hyperbolics in \(Sl(3,{\mathbb{Z}})\) (English)
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1986
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The author gives an arithmetic form of the hyperbolic terms in the Selberg trace formula for \(SL_ 3({\mathbb{Z}})\). The sum is over certain orders generated by units and is weighted by the class numbers of these orders. The author also gives a diophantine criterion for the existence of a cubic field of discriminant d; note that the form of this given in Theorem 2 suffers from an obvious misprint.
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totally real cubic fields
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hyperbolic terms
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Selberg trace formula
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class numbers
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diophantine criterion
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