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