title: The expected number of roots of random polynomials over the p-adic numbers
abstract: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 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).