Main topic of the talk is the distribution of critical values of Dirichlet -functions. I will first review previous results on mod reduction of the values. A main result of the talk is the Zariski denseness of the complex -values. One consequence of the result is the algebraic independence of the Kubota-Leopoldt -adic -functions. This can be regarded as a -adic version of algebraic independence of Dirichlet -functions, which is deduced from the joint universality of the -functions.