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Seminários do IMPA

Colóquio de Alunos

Counting squarefree values of polynomials
Cristian González Riquelme

Sexta-feira, 5 de outubro de 2018, 15:30
Sala 347

Trying to understand the asymptotic behavior of some (interesting) arithmetic subsets of the integers is one of the major motivations of Analytic Number Theory. In this introductory talk I will discuss the following problem: given a polynomial f with integer coefficients, what is the asymptotic behavior of the set of positive integers n such that f(n) is square-free? (i.e. f(n) is divisible by no perfect squares other than 1). I will introduce the basic tools, prove some basic facts, and talk a little about the history and current state of this problem.