UCLA Math Distinguished Lecture Series: Manjul Bhargava, May 20, 2015

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Lecture 2: How likely is it for an integer polynomial to take a square value?

Understanding whether (and how often) a mathematical expression takes a square value is a problem that has fascinated mathematicians since antiquity. After giving a survey of this problem, we will then concentrate on the case where the mathematical expression in question is simply a polynomial in one variable. The main result in this case - proved just recently - is that if the degree of the polynomial is at least 6, then it is not very likely to take even a single square value!

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