An explicit form of genus character $L$‐functions of quadratic orders is presented in full generality. As an application, we generalize a formula due to Hirzebruch and Zagier on the class number of imaginary quadratic fields expressed in term of the continued fraction expansion.

中文翻译：

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二次序和类号的属字L函数

属字的显式形式 $\mathrm{大号}$二次订单的功能已全面介绍。作为应用，我们将Hirzebruch和Zagier的公式推广到用连续分数展开表示的虚二次场的类数上。