Picard群在Q（i，\surd 3）上作用的陪集图
Coset Diagram for the Action of Picard Group on Q(i,\surd3)
摘要：
Picard群Γ是PSL（2，Z[i]）。我们定义了皮卡德群的陪集图。在\mathbb{Q}（i）上，Q（i，/surd 3）的某些形式为（（a+b/surd 3）/c）的元素及其共轭（（a-b/surd 3）/c）在Γ作用于双二次域Q（i，/surd 3）的陪集图中具有不同的符号，这些称为二义数.我们注意到，在陪集图中，Γ作用于\mathbb{Q}（i，/surd 3）的不确定数形成了一个唯一的模式。证明了在轨道Γα中有有限个模糊数，其中α是模糊的，它们构成一条闭路，并且它是轨道Γα中唯一的闭路.本文设计了一个求（（a+k/surd ~ 3）/c）型二义数的方法，其中k是正整数。
英文摘要：
The Picard group Γ is PSL(2,Z[i]). We have defined coset diagram for the Picard group. It has been observed that some elements of Q(i,/surd3) of the form ((a+b/surd3)/c) and their conjugates ((a-b/surd3)/c) over \mathbb{Q}(i) have different signs in the coset diagram for the action of Γ on the biquadratic field Q(i,/surd3), these are called ambiguous numbers. We have noticed that ambiguous numbers in the coset diagram for the action of Γ on \mathbb{Q}(i,/surd3) form a unique pattern. It has been shown that there are finite number of ambiguous numbers in an orbit Γα, where α is ambiguous, and they form a closed path and it is the only closed path in the orbit Γα. We have devised a procedure to obtain ambiguous numbers of the form ((a+k/surd3)/c), where k is a positive integer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
