Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the size of Nikodym sets in spaces over rings   A Nikodym set $\mathcal{N}\subseteq(\mathbb{Z}/(N\mathbb{Z}))^n$ is a set
containing $L\setminus\{x\}$ for every $x\in(\mathbb{Z}/(N\mathbb{Z}))^n$,
where $L$ is a line passing through $x$. We prove that if $N$ is square-free,
then the size of every Nikodym set is at least $c_nN^{n-o(1)}$, where $c_n$
only depends on $n$. This result is an extension of the result in the finite
field case.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con