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The shortest vector problem and tame kernels of cyclotomic fields
Journal of Number Theory ( IF 0.7 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.jnt.2021.03.022
Long Zhang , Kejian Xu , Zhaopeng Dai , Chaochao Sun

The Shortest Vector Problem and the computation of the tame kernel in algebraic K-theory are two different but very important problems, and up to now no one has found any manipulated relations between them. In this paper, we are successful for the first time to reduce the computation of tame kernel, in particular the computation of elements of the set Cm, the key part in the method proposed by Tate, to the Shortest Vector Problem of some lattice. Then, with the help of PARI library we implement the above idea and develop a program for computing the tame kernels of the cyclotomic fields with class number 1, and as an example, by running the program we obtain the tame kernel of the cyclotomic field Q(ζ7).



中文翻译:

最短的向量问题和圈域的驯服核

最短向量问题和代数K-理论中的驯服核的计算是两个不同但非常重要的问题,到目前为止,还没有人发现它们之间有任何可操纵的关系。在本文中,我们首次成功减少了驯服内核的计算,特别是减少了集合元素的计算C是Tate提出的方法的关键部分,它解决了某些晶格的最短向量问题。然后,在PARI库的帮助下,我们实现了上述想法,并开发了一个用于计算类别为1的圆环场的驯服内核的程序,并以一个示例为例,通过运行该程序,获得了圆环场的驯服内核。ζ7

更新日期:2021-05-12
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