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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.