Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Point Counting Algorithm for Cyclic Covers of the Projective Line   We present a Kedlaya-style point counting algorithm for cyclic covers $y^r =
f(x)$ over a finite field $\mathbb{F}_{p^n}$ with $p$ not dividing $r$, and $r$
and $\deg{f}$ not necessarily coprime. This algorithm generalizes the
Gaudry-G\"urel algorithm for superelliptic curves to a more general class of
curves, and has essentially the same complexity. Our practical improvements
include a simplified algorithm exploiting the automorphism of $\mathcal{C}$,
refined bounds on the $p$-adic precision, and an alternative pseudo-basis for
the Monsky-Washnitzer cohomology which leads to an integral matrix when $p \geq
2r$. Each of these improvements can also be applied to the original
Gaudry-G\"urel algorithm. We include some experimental results, applying our
algorithm to compute Weil polynomials of some large genus cyclic covers.

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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat