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SUMMARY:Ahmed Sebbar (Chapman University)
DTSTART:20220218T223000Z
DTEND:20220218T233000Z
DTSTAMP:20260423T021725Z
UID:ags/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ags/13/">On 
 a question of J. P. Serre</a>\nby Ahmed Sebbar (Chapman University) as par
 t of Analysis and Geometry Seminar\n\n\nAbstract\nIn his Bourbaki talk "{\
 \em Distribution asymptotique des valeurs propres des endomorphismes de Fr
 obenius (d'après Abel\, Chebyshev\, Robinson\,$\\cdots)$}" of 03/31/2018\
 , J.P. Serre raised the following question: \n\nLet $K\\subset \\BC$ be a 
 compact (infinite) set\, stable  under complex conjugation and having a ca
 pacity greater than one. Let $U$ be an open set containing $K$. Then there
  exists a sequence of monic polynomials $P_n(X)\\in \\BZ[X]$\, ${\\rm deg}
  P_n= n\,\\\; P_n^{-1}(0)\\subset U$ and \n\n\\[\\displaystyle \\lim_{n\\t
 o \\infty} \\frac{1}{n} \\sum_{P_n(z)=0} \\delta_z= \\mu\n\\]\n where $\\m
 u$ is the equilibrium measure of $K$ and $\\delta_z$ is the Dirac measure 
 at $z$. \\\\ I will present some results  on this question\, obtained with
  Th\\'er\\`ese Falliero(University of Avignon).\n
LOCATION:https://researchseminars.org/talk/ags/13/
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