Algebraic Properties of Shintani's Generating Functions: Dedekind Sums and Cocycles on PGL2(Q)
Algebraic Properties of Shintani's Generating Functions: Dedekind Sums and Cocycles on PGL2(Q)
复制标题
Shintani 生成函数的代数性质：PGL2(Q) 上的 Dedekind 和与余循环
DOI：
10.1023/a:1000493903703
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发表时间：
1998
影响因子：
1.8
通讯作者：
D. Solomon
中科院分区：
文献类型：
--
作者：
D. Solomon
我们引入了二元形式幂级数的某些商，称为Shintani函数。它们推广了实二次域上部分函数的特殊值的母函数[Sh]。通过对其形式性质的研究，可以快速、非解析地证明广义Dedekind和的一些结果(互易律等)。给出了群PGL2(Q)上某些1-上循环的代数构造，类似于R.Sczech和G.Stevens用解析方法构造的代数构造.数学科目分类(1991)：小学：11F20；中学：11R42。
We introduce certain quotients of two-variable formal power series, called ‘Shintani Functions’. They generalise the generating functions of [Sh] for special values of partial -functions over real quadratic fields. A study of their formal properties leads to quick, non-analytic proofs of some results on generalised Dedekind sums (Reciprocity Law, etc.). It also gives an algebraic construction of certain 1-cocycles on the group PGL 2(Q) similar to those constructed by R. Sczech and G. Stevens using analytic methods. Mathematics Subject Classifications ( 1991):Primary: 11F20; Secondary: 11R42.