We study joint equidistribution of rational points on expanding closed horocycles related by different powers using methods from analytic number theory. By applying the spectral theory of automorphic forms, we reformulate this problem in L-functions of automorphic forms twisted by characters. Our approach makes explicit the error bound in a recent work of Aka, Einsiedler, Luethi, Michel, and Wieser. This talk is based on joint work in progress with Bingrong Huang and Andreas Strömbergsson.