Rajchman measures on generalizations of the Liouville numbers

In 1980, Kaufman constructed a measure supported on the set of badly approximable numbers whose Fourier transform decays at a polynomial rate. In this talk, we will discuss a modification of Kaufman’s argument to construct Rajchman measures supported on sets of numbers having an infinite sequence of partial quotients satisfying a general type of condition. This generalizes a result of Bluhm, who constructed such measures on the set of Liouville numbers.