For any quadratic orders, we explicitly calculate the genus character L-functions in full generality.  This generalizes our old computation related to the Chowla-Selberg formula for non-fundamental orders.    

As an application, we generalize a formula due to Hirzebruch-Zagier which expresses the class numbers of some imaginary quadratic fields in terms of continued fraction expansions of suitable quadratic numbers. This is a joint work with Yoshinori Mizuno.