Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Residue Symbol   Given a prime number $l$ and a finite set of integers $S=\{a_1,...,a_m\}$ we
find out the exact degree of the extension
$\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$. We give an
algorithm to compute this degree and then further relate it to the study of the
distribution of primes $p$ for which all of $a_i$ assume a preassigned $l^{th}$
power residue simultaneously. Also we relate this degree to rank of a matrix
obtained from $S=\{a_1,...,a_m\}$. This latter arguement enable one to describe
the degree $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$ in
much simpler terms.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat