Contribution to uniform Diophantine approximation via continued fractions

Abstract: Diophantine approximation is a branch of number theory which is concerned with the question of how well can an irrational number be approximated by a rational? One of the major ingredients to study problems in Diophantine approximation is continued fraction expansion as they provide quick and efficient way for finding good rational approximations to irrational numbers. I will discuss the relationship between Diophantine approximation and the theory of continued fractions. And along the way I will talk about some measure theoretic results including the landmark results of Dirichlet (1842), Khintchine (1924), and Jarnik (1931) theorems to the questions in continued fractions. These enable us to improve the classical results by using continued fractions.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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