Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Number of Roots of a Random Polynomial over The Field of $p$-adic
  Numbers   We study the roots of a random polynomial over the field of p-adic numbers.
For a random monic polynomial with coefficients in $\mathbb{Z}_p$, we obtain an
asymptotic formula for the factorial moments of the number of roots of this
polynomial. In addition, we show the probability that a random polynomial of
degree $n$ has more than $\log n$ roots is $O\big(n^{-K}\big)$ for some $K >
0$.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph