Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divisibility of class numbers of imaginary quadratic function fields by
  a fixed odd number   In this paper we find a new lower bound on the number of imaginary quadratic
extensions of the function field $\mathbb{F}_{q}(x)$ whose class groups have
elements of a fixed odd order. More precisely, for $q$, a power of an odd
prime, and $g$ a fixed odd positive integer $\ge 3$, we show that for every
$\epsilon >0$, there are $\gg q^{L(1/2+\frac{3}{2(g+1)}-\epsilon)}$ polynomials
$f \in \mathbb{F}_{q}[x]$ with $\deg f=L$, for which the class group of the
quadratic extension $\mathbb{F}_{q}(x, \sqrt{f})$ has an element of order $g$.
This sharpens the previous lower bound $q^{L(1/2+\frac{1}{g})}$ of Ram Murty.
Our result is a function field analogue to a similar result of Soundararajan
for number fields.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an