Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of points on hyperelliptic curves   Fix a hyperelliptic curve $C/\mathbb{Q}$ of genus $g$, and consider the
number fields $K/\mathbb{Q}$ generated by the algebraic points of $C$. In this
paper, we study the number of such extensions with fixed degree $n$ and
discriminant bounded by $X$. We show that when $g \geq 1$ and $n$ is
sufficiently large relative to the degree of $C$, with $n$ even if $\deg C$ is
even, there are $\gg X^{c_n}$ such extensions, where $c_n$ is a positive
constant depending on $g$ which tends to $1/4$ as $n \to \infty$. This result
builds on work of Lemke Oliver and Thorne, who in the case where $C$ is an
elliptic curve put lower bounds on the number of extensions with fixed degree
and bounded discriminant over which the rank of $C$ grows with specified root
number.

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: physics