Squarefree values of polynomial discriminants
Recent developments in Analytic Number Theory May 01, 2017  May 05, 2017
Location: SLMath: Eisenbud Auditorium
sieve theory
Ekedahl Sieve
monogenic number fields
polynomial discriminants
geometry of numbers
11E20  General ternary and quaternary quadratic forms; forms of more than two variables
11S40  Zeta functions and $L$Lfunctions [See also 11M41, 19F27]
Bhargava
The question as to whether there exist a positive proportion of monic irreducible integral polynomials of degree n having squarefree discriminant is an old one; an exact formula for the density was conjectured by Lenstra. (The interest in monic irreducible polynomials f with squarefree discriminant comes from the fact that in such cases
Z[x]/(f(x)) gives the ring of integers in the number field Q[x]/(f(x)).)
In this talk, we describe recent work with Arul Shankar and Xiaoheng Wang that allows us to determine the probability that a random monic integer polynomial has squarefree discriminant  thus proving the conjecture of Lenstra.
Bhargava Notes

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