Centro De Giorgi – SNS.<\/p>\n
The fundamental objective of the theory of Diophantine approximation is to seek an answer to a simple question \u201chow well irrational numbers can be approximated by rational numbers?\u201d In this regard the theory of continued fractions provides a quick and efficient way for finding good rational approximations to irrational numbers.<\/span><\/span><\/p>\n 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\u2019s theorem, Khintchine\u2019s theorem and Jarnik\u2019s 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.<\/span><\/span><\/p>\n Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" The fundamental objective of the theory of Diophantine approximation is to seek an answer to a simple question \u201chow well irrational numbers can be approximated by rational numbers?\u201d In this regard the theory of continued fractions provides a quick…<\/p>\n