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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 - Xavier Caruso (CNRS)
- Tuesday 30 October 2018, 14:30-15:30
- MR13.
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. ## This talk is included in these lists:- All CMS events
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