Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence results for primitive elements in cubic and quartic extensions
  of a finite field   With $\Fq$ the finite field of $q$ elements, we investigate the following
question. If $\gamma$ generates $\Fqn$ over $\Fq$ and $\beta$ is a non-zero
element of $\Fqn$, is there always an $a \in \Fq$ such that $\beta(\gamma + a)$
is a primitive element? We resolve this case when $n=3$, thereby proving a
conjecture by Cohen. We also improve substantially on what is known when $n=4$.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga