Let K be an imaginary quadratic field with class number one and let [Special characters omitted.] be a degree one prime ideal of norm p not dividing 6 d K . In this thesis we generalize an algorithm of Schoof to compute the class number of ray class fields [Special characters omitted.] heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura\u27s reciprocity law. We have discovered a very interesting phenomena where p divides the class number of [Special characters omitted.] . This is a counterexample to the elliptic analogue of a well-known conjecture, namely the Vandiver\u27s conjecture.
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机译:令K为一类虚数二次场,令[省略特殊字符]为范数p不除6 d K的一阶素理想。在本文中,我们推广了一种Schoof算法,用于启发式地计算射线类别字段的类别数量[省略特殊字符。我们通过使用Stark解析构造的椭圆单元以及Shimura的对等定律给出的Galois作用来实现这一目标。我们发现了一个非常有趣的现象,其中p划分了[省略特殊字符]的类数。这是对已知猜想的椭圆类似物即Vandivers猜想的反例。
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