Transference principle in Diophantine approximation
(Moscow State University)
Torsdag 1. november 2018
Aud. D4 (1531-219)
In many areas of mathematics there are problems that are in some sense dual. And knowing something about one problem gives certain information concerning the dual one. In the theory of Diophantine approximation this phenomenon is demonstrated by the so called transference principle. It is most simply formulated for Diophantine exponents, the quantities generalizing the irrationality exponent of a real number responsible for how well this number can be approximated with rationals. We will talk about various Diophantine exponents and corresponding transference theorems, including the famous Khintchine's transference inequalities. We will also show how to split those inequalities into a chain of inequalities between intermediate Diophantine exponents.