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SUMMARY:Yong-Gao Chen (Nanjing Normal University\,  P. R. China)
DTSTART:20200603T130000Z
DTEND:20200603T132500Z
DTSTAMP:20260423T011219Z
UID:CANT2020/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/29/
 ">On a problem of Erdos\,  Nathanson and  Sarkozy</a>\nby Yong-Gao Chen (N
 anjing Normal University\,  P. R. China) as part of Combinatorial and addi
 tive number theory (CANT 2021)\n\n\nAbstract\nIn 1988\, Erdős\,  Nathanso
 n and  Sárközy proved that if $A$ is a\nset of nonnegative integers with
  lower asymptotic density\n$1/k$\, where $k$ is a positive integer\, then 
 $(k+1) A$ must\ncontain an infinite arithmetic progression with difference
  at most\n$ k^2-k$\, where $(k+1) A$ is the set of all sums of $k+1$ eleme
 nts\nof $A$.  They asked if $(k+1)A$ must contain an infinite arithmetic\n
 progression with difference at most $O(k)$. In this talk\, we\nanswer this
  problem negatively by proving that\, for every\nsufficiently large intege
 r $k$\, there exists a set $A$ of\nnonnegative integers with the lower asy
 mptotic density $1/k$ such\nthat  $(k+1)A$ does not contain an infinite ar
 ithmetic progression\nwith difference less than $k^{1.5}$.  \n\nJoint work
  with Ya-Li Li.\n
LOCATION:https://researchseminars.org/talk/CANT2020/29/
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