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SUMMARY:Max Wenqiang Xu (Stanford)
DTSTART:20220216T150000Z
DTEND:20220216T160000Z
DTSTAMP:20260423T021312Z
UID:WAC/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WAC/59/">Pro
 duct sets of arithmetic progressions</a>\nby Max Wenqiang Xu (Stanford) as
  part of Webinar in Additive Combinatorics\n\n\nAbstract\nWe prove that th
 e size of the product set of any finite arithmetic progression A in intege
 rs of size N is at least N^{2}/(log N)^{c+o(1)}\, where c=1-(1+loglog 2)/(
 log 2).  This matches the bound in the celebrated Erdos multiplication tab
 le problem\, up to a factor of (log N)^{o(1)} and thus confirms a conjectu
 re of Elekes and Ruzsa.\nIf instead A is relaxed to be a subset of a finit
 e arithmetic progression in integers with positive constant density\, we p
 rove that the size of the product set is at least N^{2}/(log N)^{2log2-1 +
  o(1)}. This solves the typical case of another conjecture of Elekes and R
 uzsa on the size of the product set of a set A whose sum set is of size  O
 (|A|).This is joint work with Yunkun Zhou.\n
LOCATION:https://researchseminars.org/talk/WAC/59/
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