Diophantine Approximation in local function fields via Bruhat-Tit trees

We use the theory of arithmetic quotients of the Bruhat-Tits tree developedby Serre and others to obtain Dirichlet-style theorems for Diophantineapproximation on global function fields. This approach allows us to find sharpvalues for the constants involved and, occasionally, explicit examples of badlyapproximable quadratic irrationals. Additionally, we can use this method toeasily compute the measure of the set of elements that can be written as thelimit of a sequence of ``better than expected'' approximants. All these resultscan be easily obtained via continued fractions when they are available, so thatquotient graphs can be seen as a partial replacement of them when this fails tobe the case.