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SUMMARY: Where are the zeroes of a random p-adic polynomial? - Xavier Caru
 so (CNRS)
DTSTART:20181030T143000Z
DTEND:20181030T153000Z
UID:TALK110890@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:In this talk\, I will focus on the average number of roots of 
 a\nrandom p-adic polynomials in Q_p and in their algebraic\nextensions.\nI
  will notably prove that a random p-adic polynomial has exactly\none root 
 in Q_p on average but that it has all its roots \nexcept about 2/p (still 
 on average) in the maximal unramified \nextension of Q_p. Going further\, 
 I will show that the \naverage number of roots outside the maximal tamely 
 ramified extension\nof Q_p is equivalent to 1/p^(p-2).
LOCATION:MR13
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