Metric theory of the weighted products of partial quotients in continued fractions

by Dr Ayreena Bakhtawar (Centro De Giorgi - SNS)

Wednesday 23 Nov 2022, 15:00 → 16:00 Europe/Rome

Centro De Giorgi - SNS

The fundamental objective of the theory of Diophantine approximation is to seek an answer to a simple question “how well irrational numbers can be approximated by rational numbers?” In this regard the theory of continued fractions provides a quick and efficient way for finding good rational approximations to irrational numbers.

 In this talk, first I will discuss the relationship between Diophantine approximation and the theory of continued fractions. I relate the three fundamental theories in metric Diophantine approximation (Dirichlet’s theorem, Khintchine’s theorem and Jarnik’s theorem) to the questions in continued fractions. Then I will describe some metrical properties of the product of consecutive partial quotients raised to different powers in continued fractions. This is a joint work with Mumtaz Hussain, Dmitry Kleinbock and Bao-Wei Wang.