University of Cambridge > Talks.cam > Number Theory Seminar >  Where are the zeroes of a random p-adic polynomial?

Where are the zeroes of a random p-adic polynomial?

Add to your list(s) Download to your calendar using vCal

  • UserXavier Caruso (CNRS)
  • ClockTuesday 30 October 2018, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jack Thorne.

In this talk, I will focus on the average number of roots of a random p-adic polynomials in Q_p and in their algebraic extensions. I will notably prove that a random p-adic polynomial has exactly one root in Q_p on average but that it has all its roots except about 2/p (still on average) in the maximal unramified extension of Q_p. Going further, I will show that the average number of roots outside the maximal tamely ramified extension of Q_p is equivalent to 1/p^(p-2).

This talk is part of the Number Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity