Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Roots of Polynomials Over Prime Power Rings   Suppose $p$ is a prime, $t$ is a positive integer, and
$f\!\in\!\mathbb{Z}[x]$ is a univariate polynomial of degree $d$ with
coefficients of absolute value $<\!p^t$. We show that for any fixed $t$, we can
compute the number of roots in $\mathbb{Z}/(p^t)$ of $f$ in deterministic time
$(d+\log p)^{O(1)}$. This fixed parameter tractability appears to be new for
$t\!\geq\!3$. A consequence for arithmetic geometry is that we can efficiently
compute Igusa zeta functions $Z$, for univariate polynomials, assuming the
degree of $Z$ is fixed.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con