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On the size of Nikodym sets in spaces over rings

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 نشر من قبل Chengfei Xie
 تاريخ النشر 2020
  مجال البحث
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A Nikodym set $mathcal{N}subseteq(mathbb{Z}/(Nmathbb{Z}))^n$ is a set containing $Lsetminus{x}$ for every $xin(mathbb{Z}/(Nmathbb{Z}))^n$, 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.



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