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1. CMB 2001 (vol 44 pp. 398)

Cardon, David A.; Ram Murty, M.
Exponents of Class Groups of Quadratic Function Fields over Finite Fields
We find a lower bound on the number of imaginary quadratic extensions of the function field $\F_q(T)$ whose class groups have an element of a fixed order. More precisely, let $q \geq 5$ be a power of an odd prime and let $g$ be a fixed positive integer $\geq 3$. There are $\gg q^{\ell (\frac{1}{2}+\frac{1}{g})}$ polynomials $D \in \F_q[T]$ with $\deg(D) \leq \ell$ such that the class groups of the quadratic extensions $\F_q(T,\sqrt{D})$ have an element of order~$g$.

Keywords:class number, quadratic function field
Categories:11R58, 11R29

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