A generalization of the Ross symbols in higher K-groups and hypergeometric functions I

A generalization of the Ross symbols in higher K-groups and hypergeometric functions II

This is a sequel of the paper "A generalization of the Ross symbols in higher K-groups and hypergeometric functions I" where we introduced higher Ross symbols in higher $K$-groups of the hypergeometric schemes, and discussed the Beilinson regulators. In this paper we give its p-adic counterpart and an application to the $p$-adic Beilinson conjecture for K3 surfaces of Picard number 20.

CM椭圆曲线的$L$-函数与广义超几何函数

$L$-function of CM elliptic curves and generalized hypergeometric functions

本研究通过比较动机上同调群中的Bloch元与Ross元，建立了与费马曲线相关的CM椭圆曲线$L$-函数特殊值和广义超几何函数特殊值的关联，为数论中$L$-函数特殊值计算提供新途径。

Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series

We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol step functions. This provides suitable $q$-analogs of two results proved by Christol: a formula for the $p$-adic valuation of Pochhammer symbols and a criterion for the $N$-integrality of hypergeometric series.

动力仿射量子群$U_{q,x}(\widehat{sl_2})=U_{q,λ}(\widehat{sl_2})$和超几何函数的表示

Representations of the Dynamical Affine Quantum Group $U_{q,x}(\widehat{sl_2})=U_{q,λ}(\widehat{sl_2})$ and Hypergeometric Functions

建立了Hopf代数体$U_{q,x}(\widehat{sl_2})=U_{q,λ}(\widehat{sl_2})$的表示论，证明了动力学求值模的张量积之间的缠绕是一个平衡的$_{10}W_9$符号，证实了Konno的一个猜想，即椭圆$_{12}V_{11}$级数退化为$_{10}W_9$，椭圆代数$U_{q,p}(\widehat{sl_2})$退化为$p \to 0$，基于$U_{q,x}(\widehat{sl_2})$的表示论可以证明.

四面体（或 $6j$）符号

The Tetrahedral (or $6j$) Symbol

本文研究了四面体边标记为三元正交群不可约表示的标量不变量，推广了$6j$符号理论，并展示了其与韦伊群的对称性及相对朗兰兹对偶性的关系。

划分统计量与拟弱Maass型

Partition statistics and quasiweak Maass forms

Andrews最近引入了k标记的Durfee符号，它是与Dyson的秩统计量的矩相连接的分区的推广。他用这些联系，以找到身份有关其生成功能，以及证明拉马努金型同余这些对象，并找到之间的关系。本文证明了这些对象的超几何生成函数是拟拟θ函数的自然例子，拟θ函数被定义为弱Maass形式及其导数的全纯部分。特别地，这些生成函数可以被视为具有任意高权重的Ramanujan模拟θ函数的类似物。我们利用自守性质证明了Durfee符号的无穷多个同余的存在性。此外，我们表明，随着k的变化，模块化的k-标记Durfee符号的情况下，k=2正是决定。最后，我们利用这一关系证明了秩矩在有界权的一级模形式下的一般同余的存在性。