论文标题
关于史蒂文哈根的猜想
On Stevenhagen's conjecture
论文作者
论文摘要
我们使用我们最近开发的对$ 2美元的多Qualadratic领域组的$ 2 $转换的描述来概括一项经典的互惠法。然后，该结果用于证明课程组的各种新反思原则，其中一个涉及类似于弗里德兰德（Friedlander），伊瓦尼克（Iwaniec），马祖尔（Mazur）和鲁宾（Rubin）在工作中定义的旋转符号的符号。我们将这些反思原则与史密斯的技术相结合，以证明史蒂文哈根对负pel方程的溶解度的猜想。
We generalize a classical reciprocity law due to Rédei using our recently developed description of the $2$-torsion of class groups of multiquadratic fields. This result is then used to prove a variety of new reflection principles for class groups, one of which involves a symbol similar to the spin symbol as defined in work of Friedlander, Iwaniec, Mazur and Rubin. We combine these reflection principles with Smith's techniques to prove Stevenhagen's conjecture on the solubility of the negative Pell equation.
