Invariants of 3-manifolds and Dedekind sums

首席研究员研究了广义Dedekind和与模形式之间的关系。这些都与流形的拓扑不变量密切相关。在其题为《模形式、广义Dedekin符号和周期多项式》的论文中，作者阐明了这三个对象之间的关系，并将该理论应用于典型的模形式--Eisenstein级数。在他的“广义Dedekin符号与Elsenstein级数相关”一文中，他证明了与Bisenstein级数相关的Dedekin符号本质上是Apostol的S和。他发表了题为《周期多项式空间》的论文，指出周期多项式是用伯努利多项式来表示的。这似乎非常有趣。最近，他试图将Dedekin符号定义为更广泛的形式类别，并预印了两本：《与Jacobi形式相关的Dedekin符号及其互易律》和《扭曲的广义Dedekin符号》

The head investigator have studied the relationship between generalized Dedekind sums and modular forms. These are closely related to topological invariants of manifolds. In his paper titled "Modular forms, generalized Dedekind symbols and period polynomials", the investigator clarified the relationship between these three objects.He also applied the theory to the typical modular form -- the Eisenstein series. In his paper "Generalized Dedekind symbols associated with the Elsenstein series", he proved that Dedekind symbol associated with Bisenstein series is Apostol' s sums in essence. The paper will be published soon.He published the paper tided "The space of period polynomials" which shows that period polynomials are expressed in terms of Bernoulli polynomials. This seems very interesting.Recently he is trying to define Dedekind symbols to broader class of forms and made two preprint : "Dedekind symbols associated with Jacobi forms and their reciprocity law" and "twisted generalized Dedekind symbols"