There is a classical problem of estimating the expected number of real roots of a random polynomial, going back at least to Littlewood-Offord. In this talk we shall present a p-adic version of this problem and a result estimating of the expected number of roots for a general family of distributions, and several corollaries of the theorem for specific distributions such as a random Littlewood polynomial (polynomial whose coefficients are +1 or -1).
This video was produced by Tel Aviv University as part of its algebra seminar.
