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Search: MSC category 11R58 ( Arithmetic theory of algebraic function fields [See also 14-XX] )

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1. CMB 2006 (vol 49 pp. 448)

Pacelli, Allison M.
A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by $n$
In this paper, we find a lower bound on the number of cyclic function fields of prime degree~$l$ whose class numbers are divisible by a given integer $n$. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible by $n$.

Categories:11R29, 11R58

2. 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

3. CMB 2000 (vol 43 pp. 282)

Boston, Nigel; Ose, David T.
Characteristic $p$ Galois Representations That Arise from Drinfeld Modules
We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an appropriate Drinfeld module.

Categories:11G09, 11R32, 11R58

4. CMB 1997 (vol 40 pp. 385)

Bae, Sunghan; Kang, Pyung-Lyun
Elliptic units and class fields of global function fields
Elliptic units of global function fields were first studied by D.~Hayes in the case that $\deg\infty$ is assumed to be $1$, and he obtained some class number formulas using elliptic units. We generalize Hayes' results to the case that $\deg\infty$ is arbitrary.

Categories:11R58, 11G09

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