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SUMMARY:Bo-Hae Im (Korea Advanced Institute of Science and Technology)
DTSTART:20200603T010000Z
DTEND:20200603T013000Z
DTSTAMP:20260419T091416Z
UID:NTOC2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/2/"
 >Waring’s problem for rational functions in one variable</a>\nby Bo-Hae 
 Im (Korea Advanced Institute of Science and Technology) as part of Number 
 Theory Online Conference 2020\n\n\nAbstract\nLet $f\\in \\mathbb{Q}(x)$ be
  a non-constant rational function.  We consider "Waring's Problem for $f(x
 )$"\, i.e.\, whether every element of $ \\mathbb{Q}  $ can be written as a
  bounded sum of elements of $\\{f(a)\\mid a\\in  \\mathbb{Q} \\}$.  For ra
 tional functions of degree $2$\, we give necessary and sufficient conditio
 ns.  For higher degrees\, we prove that every polynomial of odd degree and
  every odd Laurent polynomial satisfies Waring's Problem.  We also conside
 r the 'Easier Waring's Problem': whether every element of $  \\mathbb{Q} $
  can be  represented as a bounded sum of elements of $\\{\\pm f(a)\\mid a\
 \in \\mathbb{Q}  \\}$. This is a joint work with Michael Larsen.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/2/
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