Squarefree sieves in arithmetic statistics

Abstract: A classical question in analytic number theory is: given a polynomial with integer coefficients, how often does it take squarefree values? In arithmetic statistics, we are particularly interested in the case of discriminant polynomials. In this talk, I will present several different cases of this question. First, we will consider a classical result of Davenport--Heilbronn which considers the case of discriminants of binary cubic forms. Then, I will discuss joint work with Bhargava in which we consider the case of discriminants of ternary cubic forms.

Third, I will describe joint and ongoing work with Bhargava and Wang, in which we consider different families of degree-n polynomials in one variable, and determine the proportion of those having squarefree discriminant. Finally, I will describe various applications of these results

number theory

Audience: researchers in the topic

CMI seminar series

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