Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of polynomials with prescribed range   We show that, for any integer $\ell$ with $q-\sqrt{p} -1 \leq \ell < q-3$
where $q=p^n$ and $p>9$, there exists a multiset $M$ satisfying that $0\in M$
has the highest multiplicity $\ell$ and $\sum_{b\in M} b =0$ such that every
polynomial over finite fields $\fq$ with the prescribed range $M$ has degree
greater than $\ell$. This implies that Conjecture 5.1. in \cite{gac} is false
over finite field $\fq$ for $p > 9$ and $k:=q-\ell -1 \geq 3$.

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat