BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART:20201012T111500Z
DTEND:20201012T121500Z
DTSTAMP:20260423T022143Z
UID:WarsawNT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/7/"
 >Solution of the conjecture of Schinzel and Zassenhaus and some applicatio
 ns</a>\nby Vesselin Dimitrov (University of Toronto) as part of Warsaw Num
 ber Theory Seminar\n\n\nAbstract\nWe will detail the full proof of an expl
 icit form of the Schinzel-Zassenhaus conjecture: an algebraic integer of d
 egree $n > 1$ is either a root of unity or else has at least one conjugate
  of modulus exceeding $2^{1/(4n)}$. We furthermore obtain an extension of 
 the original conjecture over to the setting of holonomic functions\, with 
 an application to the smallest critical value for (certain) rational funct
 ions.\n\nIn another application\, we would like to take the occasion to ra
 ise the apparently unsolved problem of the essential irreducibility (up-to
  the cyclotomic factor $X^2-X+1$ in degrees a multiple of 12) of $X^{2g} -
  X^g(1+X+1/X) + 1$\, the characteristic polynomial of the integer reciproc
 al Perron-Frobenius matrix of the smallest spectral radius in each given d
 imension. Our explicit Schinzel-Zassenhaus bound allows for at most $10$ f
 actors of each of these polynomials.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/7/
END:VEVENT
END:VCALENDAR