类域构作问题即著名的 Hilbert 第 12 问题。通过回顾悬而未决的 Hilbert 第 12 问题的百年历程，特别是 Kronecker，Weber，Takagi，Stark，Gross，Darmon，Dasgupta，Hayes，Anglès, Pellarin 等前辈对这一问题的杰出贡献，我们希望借助 Serre 关于 p-进模形式的工作，建立相应 p-进模函数和椭圆函数，并依据 Gross，Darmon 等人的想法提出明确构作全实域（或实二次域）的类域的一种思路，即提出对全实域（或实二次域）这一重要情形用p-进模形式解决Hilbert第 12 问题的一种新的思路，并分析这一思路的可行性。

The class fields construction problem is Hilbert’s twelfth problem. By reviewing one hundred years' history of Hilbert’s twelfth (open) problem, especially, by recalling Kronecker, Weber, Takagi, Stark, Gross, Darmon, Dasgupta, Hayes, Anglès, Pellarin and other predecessors’ outstanding contributions to this issue, we hope to give explicit constructions of class fields for totally real fields (or real quadartic fields) using Serre’s definitions of p-adic modular forms and Gross, Darmon’s ideas under this direction, that is, we present a new idea for solving Hilbert’s twelfth problem for totally real fields (or real quadratic fields) which will be based on p-adic modular forms.