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SUMMARY:Jin-Hui Fang (Nanjing University of Information Science and Techno
 logy)
DTSTART:20220526T130000Z
DTEND:20220526T132500Z
DTSTAMP:20260423T011437Z
UID:CANT2022/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/31/
 ">Representation functions avoiding integers with density zero</a>\nby Jin
 -Hui Fang (Nanjing University of Information Science and Technology) as pa
 rt of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\n
 For a nonempty set $A$ of integers and any integer $n$\, denote $r_{A}(n)$
  by the number of representations of $n$ of the form $n=a+a'$\, where $a\\
 le a'$ and $a\,a'\\in A$ and $d_{A}(n)$ by the number of pairs $(a\,a')$ w
 ith $a\,a'\\in A$ such that $n=a-a'$. In 2008\, Nathanson considered the r
 epresentation function with infinitely many zeros. Following Nathanson's w
 ork\, we proved that\, for any set $T$ of integers with density zero\, the
 re exists a sequence $A$ of integers such that $r_A(n)=1$ for all integers
  $n\\not\\in T$ and $r_A(n)=0$ for all integers $n\\in T$\, and $d_A(n)=1$
  for all positive integers $n$. We will also present our recent results on
  representation functions.\n
LOCATION:https://researchseminars.org/talk/CANT2022/31/
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