Exponents of Class Groups of Quadratic Function Fields over Finite Fields
نویسنده
چکیده
We find a lower bound on the number of imaginary quadratic extensions of the function field Fq(T ) whose class groups have an element of a fixed order. More precisely, let q ≥ 5 be a power of an odd prime and let g be a fixed positive integer ≥ 3. There are q 1 2+ 1 g ) polynomials D ∈ Fq[T ] with deg(D) ≤ ` such that the class groups of the quadratic extensions Fq(T, √ D) have an element of order g.
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