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Seminários do IMPA

Colóquio dos Alunos

Título
Counting squarefree values of polynomials
Expositor
Cristian González Riquelme

IMPA
Data
Sexta-feira, 5 de outubro de 2018, 15:30
Local
Sala 347
Resumo

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.