Let F/k be a finite abelian extension of number fields with k imaginary quadratic. Let O_F be the ring of integers of F and n ⩾ 2 a rational integer. We construct a submodule in the higher odd-degree algebraic K-groups of O_F using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of F, which is the cardinal of the finite algebraic K-group K_2n−2(O_F).

中文翻译：

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虚二次域上的扭曲类数公式和格罗斯特殊单位

令F/k为具有k 个虚二次的数域的有限阿贝尔扩张。设O _F为F的整数环，n ⩾ 2 为有理整数。我们使用相应的 Gross 特殊元素在OF的更高奇次代数K群中构造一个子_模。我们证明该子模块具有有限索引，并证明该索引可以使用F的较高“扭曲”类数来计算，F 是有限代数K群K _{2 n −2} ( O _F )的基数。