We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic$p$-adic $L$-functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic $p$-adic $L$-functions to more general Shimura curves.

In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on $PS{L}_2\left(\mathbb{Z}\right)\setminus PS{L}_2\left(ℝ\right)$. This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for $PS{L}_2\left(\mathbb{Z}\right)\setminus ℍ$. The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of $S{L}_2\left(ℝ\right)$. In the proof the key estimates come from applying...