Genus fields of cyclic \(l\)-extensions of rational function fields (Q2840304)
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scientific article; zbMATH DE number 6189011
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Genus fields of cyclic \(l\)-extensions of rational function fields |
scientific article; zbMATH DE number 6189011 |
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17 July 2013
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genus fields
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congruence function fields
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global fields
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cyclotomic function fields
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Kummer extensions
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cyclic extensions
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0.94229174
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0.9418726
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0.93777204
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0.9309007
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0.91629696
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0.91263443
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0.9113197
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0.9101064
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Genus fields of cyclic \(l\)-extensions of rational function fields (English)
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Let \(k\) be the field of rational functions over the finite field \(F_q\), let \(l\) be a prime and assume \(l^n\mid q-1\). The authors describe the generators of the genus field of cyclic extensions \(K/k\) of degree \(l^n\). In the case \(n=1\) this was done by \textit{G. Peng} [J. Number Theory 98, No. 2, 221--227 (2003; Zbl 1049.11116)], and another proof was provided by \textit{M. Maldonaldo-Ramirez, M. Rzedowski-Calderón} and \textit{G. Villa-Salvador} [Finite Fields Appl. 20, 40--54 (2013; Zbl 1285.11140)].
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