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

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

2010-07-10

arxiv.org/abs/1007.1729v1

Mathematics

Number Theory

Scientific paper

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.

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