It has been known for almost a hundred years that most polynomials with integral coefficients are irreducible and have a big Galois group. For a few dozen years, people have been interested in whether the same holds when one considers sparse families of polynomials—notably, polynomials with plus-minus 1 coefficients. In particular, “some guy on the street” conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity (a much earlier conjecture of Odlyzko-Poonen is about the 0-1 coefficients model). In this talk, I will discuss these types of problems and their connection with analytic number theory in particular, primes with restricted digits.
Thu, 17/01/2019 - 14:30 to 15:30
Manchester Building (Hall 2), Hebrew University Jerusalem