The Duffin-Schaeffer conjecture with extra divergence
Linfoot Number Theory Seminar
12th June 2019, 11:00 am – 12:00 pm
Howard House, 4th Floor Seminar Room
The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. Assuming a certain divergence of a series associated to the approximating function, it asserts that almost all reals can be approximated by reduced fractions. The conjecture holds under some additional restrictions on the approximated function but remains fully open in its generality. In the present talk we will review these results and show that the conjecture is true under a stronger assumption on the divergence of the series.
This is a joint work with Aistleitner, Lachmann, Technau and Zafeiropoulos.