Generalized Dedekind symbols associated with the Eisenstein series
Generalized Dedekind symbols associated with the Eisenstein series
复制标题
与爱森斯坦级数相关的广义戴德金符号
DOI：
10.1090/s0002-9939-99-05291-0
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发表时间：
1999
影响因子：
2.5
通讯作者：
S. Fukuhara
中科院分区：
文献类型：
--
作者：
S. Fukuhara
我们最近证明了模形式的空间、广义戴德金和的空间以及周期多项式的空间都是同构的。在本文中，我们将证明，在这些同构下，爱森斯坦级数对应于阿波斯托尔广义戴德金和，并且周期多项式用伯努利数表示。这为我们提供了 Apostol 广义戴德金和的互易律的新的更自然的证明。我们的证明作为副产品产生了新的多对数恒等式。
We have shown recently that the space of modular forms, the space of generalized Dedekind sums, and the space of period polynomials are all isomorphic. In this paper, we will prove, under these isomorphisms, that the Eisenstein series correspond to the Apostol generalized Dedekind sums, and that the period polynomials are expressed in terms of Bernoulli numbers. This gives us a new more natural proof of the reciprocity law for the Apostol generalized Dedekind sums. Our proof yields as a by-product new polylogarithm identities.