Diophantine Approximation is a branch of Number theory in which the central theme is understanding how well real numbers can be approximated by rationals. Dirichlet's theorem (1842) is a fundamental result that gives an optimal approximation rate of any irrational number. The set of real numbers for which Dirichlet's theorem admits an improvement was originally studied by Davenport and Schmidt. It has been recently proved that the improvements to Dirichlet's theorem are related to the growth of the products of consecutive partial quotients. In this talk I will discuss some new metrical results for the set of Dirichlet non-improvable numbers in connection with the theory of continued fractions.
Meeting ID: 852 4277 3200 Passcode: 103121