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SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20200527T151000Z
DTEND:20200527T161000Z
DTSTAMP:20260423T005846Z
UID:TAUFA/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TAUFA/3/">On
  a problem of Tur\\'an and sparse polynomials</a>\nby Michael Filaseta (Un
 iversity of South Carolina) as part of Tel Aviv field arithmetic seminar\n
 \n\nAbstract\nI will give a survey of various results associated with the 
 factorization of sparse polynomials in $\\mathbb Z[x]$.  One motivating qu
 estion that pushed some of the results to be considered is a question due 
 to P\\'al Tur\\'an:  Is there an absolute constant $C$ such that if $f(x) 
 \\in \\mathbb Z[x]$\, then there is a polynomial $g(x) \\in Z[x]$ that is 
 irreducible and within $C$ of being $f(x)$ in the sense that the sum of th
 e absolute values of the difference $f(x) - g(x)$ is bounded by $C$?  This
  is known to be true as I stated it\, but Tur\\'an also added the restrict
 ion that $\\deg g \\le \\deg f$\, and the problem remains open in this cas
 e with good evidence that such a $C$ probably does exist.\n
LOCATION:https://researchseminars.org/talk/TAUFA/3/
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