Goldfeld D M
The Institute for Advanced Study, Princeton, New Jersey 08540.
Proc Natl Acad Sci U S A. 1974 Apr;71(4):1055. doi: 10.1073/pnas.71.4.1055.
A brief and simple proof of Siegel's celebrated theorem that h(d) >> d(1/2-[unk]), as d --> infinity, is given. Here h(d) denotes the class number of the quadratic field Q([unk]-d). Simple proofs that do not make use of algebraic number theory have been previously given by Estermann and Chowla.
给出了西格尔著名定理的一个简短而简单的证明，即当(d\to\infty)时，(h(d)\gg d^{1/2 - \epsilon})，其中(h(d))表示二次域(\mathbb{Q}(\sqrt{-d}))的类数。此前埃斯特曼和乔拉已给出了不使用代数数论的简单证明。
