Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive divisors of sequences associated to elliptic curves over
  function fields   We study the existence of a Zsigmondy bound for a sequence of divisors
associated to points on an elliptic curve over a function field. More
precisely, let $k$ be an algebraically closed field, let $\mathcal{C}$ be a
nonsingular projective curve over $k$, and let $K$ denote the function field of
$\mathcal{C}$. Suppose $E$ is an ordinary elliptic curve over $K$ and suppose
there does not exist an elliptic curve $E_0$ defined over $k$ that is
isomorphic to $E$ over $K$. Suppose $P\in E(K)$ is a non-torsion point and
$Q\in E(K)$ is a torsion point of order $r$. The sequence of points
$\{nP+Q\}\subset E(K)$ induces a sequence of effective divisors $\{D_{nP+Q}\}$
on $\mathcal{C}$. We provide conditions on $r$ and the characteristic of $k$
for there to exist a bound $N$ such that $D_{nP+Q}$ has a primitive divisor for
all $n\geq N$. This extends the analogous result of Verzobio in the case where
$K$ is a number field.

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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org