Bohr sets and multiplicative diophantine approximation
Linfoot Number Theory Seminar
14th November 2018, 11:00 am – 12:00 pm
Howard House, 4th Floor Seminar Room
Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. I'll discuss some recent refinements of Gallagher's theorem, one of which is joint work with Niclas Technau. A key new ingredient is the correspondence between Bohr sets and generalised arithmetic progressions. It is hoped that these are the first steps towards a metric theory of multiplicative diophantine approximation on manifolds.