On powers of the denominators of rationals (Q795858)
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scientific article; zbMATH DE number 3863284
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On powers of the denominators of rationals |
scientific article; zbMATH DE number 3863284 |
Statements
On powers of the denominators of rationals (English)
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1983
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For rational x let \(den^{\alpha} x\) be the \(\alpha\) th power of the denominator of x, where \(\alpha\) is a fixed complex number. This function is regarded as an analogue of the inhomogeneous Dedekind sum \(D(h/k):=s(h,k)\). Formulas corresponding to the reciprocity, Petersson- Knopp and Subrahmanyam ones for D(x) are given to \(den^{\alpha} x\) after the manner of the author's paper [Acta Arith. 44, 207-214 (1984; Zbl 0512.10007)].
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Hecke operator
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averaging operator
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Möbius inversion
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generalized Dedekind sums
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reciprocity
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