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SUMMARY:Stephen D. Cohen (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20200603T131000Z
DTEND;VALUE=DATE-TIME:20200603T141000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071315Z
UID:TAUFA/2
DESCRIPTION:Title: Ex
istence theorems for primitive elements in finite fields\nby Stephen D
. Cohen (University of Glasgow) as part of Tel Aviv field arithmetic semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TAUFA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART;VALUE=DATE-TIME:20200527T151000Z
DTEND;VALUE=DATE-TIME:20200527T161000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071315Z
UID:TAUFA/3
DESCRIPTION:Title: On
a problem of Tur\\'an and sparse polynomials\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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BEGIN:VEVENT
SUMMARY:Rainer Dietmann (Royal Holloway\, University of London)
DTSTART;VALUE=DATE-TIME:20200506T131000Z
DTEND;VALUE=DATE-TIME:20200506T141000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071315Z
UID:TAUFA/4
DESCRIPTION:Title: En
umerative Galois theory for cubics and quartics\nby Rainer Dietmann (R
oyal Holloway\, University of London) as part of Tel Aviv field arithmetic
seminar\n\n\nAbstract\nThis is joint work with Sam Chow. We consider moni
c quartic polynomials with integer coefficients and growing box height at
most H. In this setting\, we exactly determine the order of magnitude (fro
m above and below) of such polynomials whose Galois group is D_4. Moreover
\, we show that C_4 and V_4 polynomials are less frequent that D_4 ones\,
and that D_4\, C_4\, V_4 and A_4 polynomials are together less frequent th
an reducible quartics. Similarly\, for integer monic cubic polynomials we
show that A_3 cubics are less frequent than reducible cubics. In particula
r\, irreducible non-S_n polynomials are less numerous than reducible ones
for n = 3 and n = 4\, for the first time solving two cases (namely degree
three and four) of a conjecture by van der Waerden from 1936.\n
LOCATION:https://researchseminars.org/talk/TAUFA/4/
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