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Galois Groups and Genera of a kind of Quasi-cyclotomic Function Fields

We call a (q-1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the structure of the Galois groups of a kind of quasi-cyclotomic function fields over the base field. We also give the genus formulae of them.

preprint2012arXivOpen access
Min ShaLinsheng Yin
math.NT
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Min ShaLinsheng Yin

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