UCLA Math Distinguished Lecture Series: Manjul Bhargava, May 21, 2015

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Lecture 3: The density of squarefree values taken by a polynomial
It is well known that the density of integers that are squarefree is 6/π2, giving one of the more intriguing occurrences of π where one might not a priori expect it! A natural next problem that has played an important role in number theory is that of understanding the density of squarefree values taken by an integer polynomial. We survey a number of recent results on this problem for various types of polynomials - some of which use the ABC Conjecture and some of which do not.

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