全实域上多项式的退化与L函数的特殊值

$p$-adic Polylogarithms and $p$-adic Hecke $L$-functions for Totally Real Fields

The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special values of $p$-adic $L$-functions interpolating nonpositive values of Hecke $L$-functions of the totally real field in terms of special values of these $p$-adic polylogarithms.

全实域的多对数霍奇实现与 Shintani 生成类

The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields

本文在关联全实域的代数环面等变 Deligne-Beilinson 上同调中构造多对数类的霍奇实现，证明其 de Rham 实现给出 Shintani 生成类，并提出关于挠点特殊化的猜想及其与 Beilinson 猜想的联系。

Topological polylogarithms and $p$-adic interpolation of $L$-values of totally real fields

We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for $GL_n(\mathbf{Z})$ and yields classes with values in an Iwasawa algebra. This implies directly the integrality properties of special values of $L$-functions of totally real fields and a construction of the associated $p$-adic $L$-function. Using a result of Graf, we also apply this to prove some integrality and $p$-adic interpolation results for the Eisenstein cohomology of Hilbert modular varieties.

Polylogarithms for $GL_2$ over totally real fields

We give a new, purely topological construction of Eisenstein cohomology classes for Hilbert-Blumenthal varieties using the polylogarithm for families of topological tori and a decomposition with respect to the units in the center of $GL_2$. These classes are explicitly calculated in de Rham chomology and compared with Harder's Eisenstein classes. For non-trivial coefficient systems the whole Eisenstein cohomology in positive degrees is generated by these topological Eisenstein classes. This gives an alternative proof for the rationality of Harder's Eisenstein operator without using any multipl…

高亏格多重zeta值

Higher-genus multiple zeta values

该研究将多重zeta值的形式体系从经典及椭圆情形规范扩展到高亏格黎曼曲面，提出基于肖特基单值化的正则化方案，探究几何退化和多重对数关系衍生的高亏格多重zeta值关系，并通过数值验证发现了新的关系类别。

黎曼曲面上平坦联络的退化

Degenerations of flat connections on Riemann surfaces

研究黎曼曲面平坦联络的退化，通过非分离退化得到多对数函数积分核封闭，给出多变量恩里克斯联络退化公式及单值DHS核类似公式，用于关联不同亏格的模张量。