In this talk we will give a broad overview of the Linnik problems concerning the equidistribution of integral points on homogeneous varieties. One particular example concerns the Heegner points, which are roots in the complex upper-half plane of certain quadratic forms. We will discuss certain "sparse" equidistribution problems concerning these points and give an application of an analog of Linnik's famous theorem on the first prime in an arithmetic progression. The resolution of these problems involves a wide-range of techniques concerning modular forms and their associated L-functions. This is joint work with Riad Masri and Matt Young.