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

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

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  • 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.

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